Lenart, Cristian; Naito, Satoshi; Orr, Daniel; Sagaki, Daisuke Inverse \(K\)-Chevalley formulas for semi-infinite flag manifolds. II: Arbitrary weights in ADE type. (English) Zbl 07681928 Adv. Math. 423, Article ID 109037, 63 p. (2023). MSC: 20C08 17B37 14M15 14N15 33D52 81R10 PDFBibTeX XMLCite \textit{C. Lenart} et al., Adv. Math. 423, Article ID 109037, 63 p. (2023; Zbl 07681928) Full Text: DOI arXiv
Kouno, Takafumi; Naito, Satoshi; Orr, Daniel; Sagaki, Daisuke Inverse \(K\)-Chevalley formulas for semi-infinite flag manifolds. I: Minuscule weights in ADE type. (English) Zbl 1527.20003 Forum Math. Sigma 9, Paper No. e51, 25 p. (2021). MSC: 20C08 17B37 14M15 19L47 33D52 81R10 PDFBibTeX XMLCite \textit{T. Kouno} et al., Forum Math. Sigma 9, Paper No. e51, 25 p. (2021; Zbl 1527.20003) Full Text: DOI arXiv
Naito, Satoshi; Orr, Daniel; Sagaki, Daisuke Chevalley formula for anti-dominant weights in the equivariant \(K\)-theory of semi-infinite flag manifolds. (English) Zbl 1515.17031 Adv. Math. 387, Article ID 107828, 59 p. (2021). Reviewer: Shintaro Yanagida (Nagoya) MSC: 17B37 14N15 14M15 33D52 81R10 PDFBibTeX XMLCite \textit{S. Naito} et al., Adv. Math. 387, Article ID 107828, 59 p. (2021; Zbl 1515.17031) Full Text: DOI arXiv
Sagaki, Daisuke; Yu, Dongxiao Path model for an extremal weight module over the quantized hyperbolic Kac-Moody algebra of rank 2. (English) Zbl 1479.17031 Commun. Algebra 49, No. 2, 690-705 (2021). Reviewer: Marijana Butorac (Rijeka) MSC: 17B37 17B67 81R50 PDFBibTeX XMLCite \textit{D. Sagaki} and \textit{D. Yu}, Commun. Algebra 49, No. 2, 690--705 (2021; Zbl 1479.17031) Full Text: DOI arXiv
Kato, Syu; Naito, Satoshi; Sagaki, Daisuke Equivariant \(K\)-theory of semi-infinite flag manifolds and the Pieri-Chevalley formula. (English) Zbl 1475.17024 Duke Math. J. 169, No. 13, 2421-2500 (2020). Reviewer: Huafeng Zhang (Villeneuve d’Ascq) MSC: 17B37 14N15 33D52 81R10 PDFBibTeX XMLCite \textit{S. Kato} et al., Duke Math. J. 169, No. 13, 2421--2500 (2020; Zbl 1475.17024) Full Text: DOI arXiv Euclid
Naito, Satoshi; Nomoto, Fumihiko; Sagaki, Daisuke Tensor product decomposition theorem for quantum Lakshmibai-Seshadri paths and standard monomial theory for semi-infinite Lakshmibai-Seshadri paths. (English) Zbl 1471.17021 J. Comb. Theory, Ser. A 169, Article ID 105122, 36 p. (2020). MSC: 17B10 05E10 17B22 17B37 PDFBibTeX XMLCite \textit{S. Naito} et al., J. Comb. Theory, Ser. A 169, Article ID 105122, 36 p. (2020; Zbl 1471.17021) Full Text: DOI arXiv
Naito, Satoshi; Nomoto, Fumihiko; Sagaki, Daisuke Representation-theoretic interpretation of Cherednik-Orr’s recursion formula for the specialization of nonsymmetric Macdonald polynomials at \(t = \infty\). (English) Zbl 1462.17020 Transform. Groups 24, No. 1, 155-191 (2019). Reviewer: Huafeng Zhang (Villeneuve d’Ascq) MSC: 17B37 17B67 05E10 33D52 PDFBibTeX XMLCite \textit{S. Naito} et al., Transform. Groups 24, No. 1, 155--191 (2019; Zbl 1462.17020) Full Text: DOI
Naito, Satoshi; Nomoto, Fumihiko; Sagaki, Daisuke Specialization of nonsymmetric Macdonald polynomials at \(t=\infty \) and Demazure submodules of level-zero extremal weight modules. (English) Zbl 1432.17015 Trans. Am. Math. Soc. 370, No. 4, 2739-2783 (2018). MSC: 17B37 33D52 PDFBibTeX XMLCite \textit{S. Naito} et al., Trans. Am. Math. Soc. 370, No. 4, 2739--2783 (2018; Zbl 1432.17015) Full Text: DOI arXiv
Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark Quantum Lakshmibai-Seshadri paths and root operators. (English) Zbl 1418.17036 Naruse, Hiroshi (ed.) et al., Schubert calculus – Osaka 2012. Proceedings of the 5th Mathematical Society of Japan-Seasonal Institute, MSJ-SI, Osaka, Japan, July 17–27, 2012. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 71, 267-294 (2016). MSC: 17B37 05E10 PDFBibTeX XMLCite \textit{C. Lenart} et al., Adv. Stud. Pure Math. 71, 267--294 (2016; Zbl 1418.17036) Full Text: arXiv
Naito, Satoshi; Sagaki, Daisuke Demazure submodules of level-zero extremal weight modules and specializations of Macdonald polynomials. (English) Zbl 1395.17029 Math. Z. 283, No. 3-4, 937-978 (2016). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Math. Z. 283, No. 3--4, 937--978 (2016; Zbl 1395.17029) Full Text: DOI arXiv
Ishii, Motohiro; Naito, Satoshi; Sagaki, Daisuke Semi-infinite Lakshmibai-Seshadri path model for level-zero extremal weight modules over quantum affine algebras. (English) Zbl 1387.17028 Adv. Math. 290, 967-1009 (2016). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{M. Ishii} et al., Adv. Math. 290, 967--1009 (2016; Zbl 1387.17028) Full Text: DOI arXiv
Lenart, Cristian; Naito, Satoshi; Sagaki, Daisuke; Schilling, Anne; Shimozono, Mark Explicit description of the degree function in terms of quantum Lakshmibai-Seshadri paths. (English) Zbl 1368.17027 Toyama Math. J. 37, 107-130 (2015). MSC: 17B67 17B37 PDFBibTeX XMLCite \textit{C. Lenart} et al., Toyama Math. J. 37, 107--130 (2015; Zbl 1368.17027) Full Text: arXiv Link
Naito, Satoshi; Sagaki, Daisuke; Saito, Yoshihisa Toward Berenstein-Zelevinsky data in affine type \(A\). III: Proof of the connectedness. (English) Zbl 1355.17013 Iohara, Kenji (ed.) et al., Symmetries, integrable systems and representations. Proceedings of the conference on infinite analysis: frontier of integrability, Tokyo, Japan, July 25–29, 2011 and the conference on symmetries, integrable systems and representations, Lyon, France, December 13–16, 2011. London: Springer (ISBN 978-1-4471-4862-3/hbk; 978-1-4471-4863-0/ebook). Springer Proceedings in Mathematics & Statistics 40, 361-402 (2013). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} et al., Springer Proc. Math. Stat. 40, 361--402 (2013; Zbl 1355.17013) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke; Saito, Yoshihisa Toward Berenstein-Zelevinsky data in affine type \(A\). II: Explicit description. (English) Zbl 1352.17019 Ariki, Susumu (ed.) et al., Algebraic groups and quantum groups. International conference on representation theory of algebraic groups and quantum groups ’10, Graduate School of Mathematics, Nagoya University, Nagoya, Japan, August 2–6, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5317-7/pbk; 978-0-8218-8536-9/ebook). Contemporary Mathematics 565, 185-216 (2012). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} et al., Contemp. Math. 565, 185--216 (2012; Zbl 1352.17019) Full Text: arXiv
Naito, Satoshi; Sagaki, Daisuke; Saito, Yoshihisa Toward Berenstein-Zelevinsky data in affine type \(A\). I: Construction of the affine analogs. (English) Zbl 1352.17018 Ariki, Susumu (ed.) et al., Algebraic groups and quantum groups. International conference on representation theory of algebraic groups and quantum groups ’10, Graduate School of Mathematics, Nagoya University, Nagoya, Japan, August 2–6, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5317-7/pbk; 978-0-8218-8536-9/ebook). Contemporary Mathematics 565, 143-184 (2012). MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} et al., Contemp. Math. 565, 143--184 (2012; Zbl 1352.17018) Full Text: arXiv
Naito, Satoshi; Sagaki, Daisuke Tensor product multiplicities for crystal bases of extremal weight modules over quantum infinite rank affine algebras of types \(B_{\infty }\), \(c_{\infty }\), and \(D_{\infty }\). (English) Zbl 1335.17007 Trans. Am. Math. Soc. 364, No. 12, 6531-6564 (2012). MSC: 17B37 17B67 17B10 05A19 05E10 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Trans. Am. Math. Soc. 364, No. 12, 6531--6564 (2012; Zbl 1335.17007) Full Text: DOI arXiv
Kato, Syu; Naito, Satoshi; Sagaki, Daisuke Tensor products and Minkowski sums of Mirković-Vilonen polytopes. (English) Zbl 1280.17018 Transform. Groups 17, No. 1, 195-207 (2012). MSC: 17B37 20G05 17B10 14M15 05E15 PDFBibTeX XMLCite \textit{S. Kato} et al., Transform. Groups 17, No. 1, 195--207 (2012; Zbl 1280.17018) Full Text: DOI arXiv
Kato, Syu; Naito, Satoshi; Sagaki, Daisuke Polytopal estimate of Mirković-Vilonen polytopes lying in a Demazure crystal. (English) Zbl 1219.17011 Adv. Math. 226, No. 3, 2587-2617 (2011). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 14M15 17B10 14L35 PDFBibTeX XMLCite \textit{S. Kato} et al., Adv. Math. 226, No. 3, 2587--2617 (2011; Zbl 1219.17011) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Crystal base elements of an extremal weight module fixed by a diagram automorphism. II: Case of affine Lie algebras. (English) Zbl 1259.17014 Gyoja, Akihiko (ed.) et al., Representation theory of algebraic groups and quantum groups. Based on the 6th international conference by the Graduate School of Mathematics on representation theory of algebraic groups and quantum groups, Nagoya, Japan, June 12–17, 2006. Boston, MA: Birkhäuser (ISBN 978-0-8176-4696-7/hbk; 978-0-8176-4697-4/ebook). Progress in Mathematics 284, 225-255 (2010). MSC: 17B37 17B10 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Prog. Math. 284, 225--255 (2010; Zbl 1259.17014) Full Text: DOI
Naito, Satoshi; Sagaki, Daisuke Mirković-Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal. (English) Zbl 1194.17008 Adv. Math. 221, No. 6, 1804-1842 (2009). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 14M15 17B10 14L35 20G10 52B12 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Adv. Math. 221, No. 6, 1804--1842 (2009; Zbl 1194.17008) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Lakshmibai-Seshadri paths of level-zero shape and one-dimensional sums associated to level-zero fundamental representations. (English) Zbl 1234.17010 Compos. Math. 144, No. 6, 1525-1556 (2008). Reviewer: Valentina Golubeva (Moskva) MSC: 17B37 81R50 82B23 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Compos. Math. 144, No. 6, 1525--1556 (2008; Zbl 1234.17010) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape. (English) Zbl 1219.17013 Proc. Lond. Math. Soc. (3) 96, No. 3, 582-622 (2008). Reviewer: Sorin Dascalescu (Bucureşti) MSC: 17B37 05E99 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Proc. Lond. Math. Soc. (3) 96, No. 3, 582--622 (2008; Zbl 1219.17013) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras. (English) Zbl 1163.17302 Commun. Math. Phys. 263, No. 3, 749-787 (2006). MSC: 17B37 05E15 81R50 82B23 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Commun. Math. Phys. 263, No. 3, 749--787 (2006; Zbl 1163.17302) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Path model for a level-zero extremal weight module over a quantum affine algebra. II. (English) Zbl 1091.17009 Adv. Math. 200, No. 1, 102-124 (2006). Reviewer: Joaquín Jódar Reyes (Jaen) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Adv. Math. 200, No. 1, 102--124 (2006; Zbl 1091.17009) Full Text: DOI arXiv
Naito, Satoshi; Sagaki, Daisuke Crystal base elements of an extremal weight module fixed by a diagram automorphism. (English) Zbl 1151.17008 Algebr. Represent. Theory 8, No. 5, 689-707 (2005). MSC: 17B37 17B10 81R50 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Algebr. Represent. Theory 8, No. 5, 689--707 (2005; Zbl 1151.17008) Full Text: DOI
Naito, Satoshi; Sagaki, Daisuke Crystal of Lakshmibai-Seshadri paths associated to an integral weight of level zero for an affine Lie algebra. (English) Zbl 1080.17009 Int. Math. Res. Not. 2005, No. 14, 815-840 (2005). Reviewer: Joaquín Jódar Reyes (Jaen) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Int. Math. Res. Not. 2005, No. 14, 815--840 (2005; Zbl 1080.17009) Full Text: DOI
Naito, Satoshi; Sagaki, Daisuke Crystal bases and diagram automorphisms. (English) Zbl 1090.17013 Shoji, Toshiaki (ed.) et al., Representation theory of algebraic groups and quantum groups. Papers from the conference held as the 10th International Research Institute of the Mathematical Society of Japan (MSJ-IRI) at Sophia University, Tokyo, Japan, August 1–10, 2001. Tokyo: Mathematical Society of Japan (ISBN 4-931469-25-6/hbk). Advanced Studies in Pure Mathematics 40, 321-341 (2004). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B67 17B37 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Adv. Stud. Pure Math. 40, 321--341 (2004; Zbl 1090.17013)
Naito, Satoshi; Sagaki, Daisuke A rationalization of the crystal \(\mathbb Z^{\infty}\) and a diagram automorphism. (English) Zbl 1084.17008 J. Pure Appl. Algebra 189, No. 1-3, 279-295 (2004). MSC: 17B37 81R50 17B67 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, J. Pure Appl. Algebra 189, No. 1--3, 279--295 (2004; Zbl 1084.17008) Full Text: DOI
Naito, Satoshi; Sagaki, Daisuke Path model for a level-zero extremal weight module over a quantum affine algebra. (English) Zbl 1080.17008 Int. Math. Res. Not. 2003, No. 32, 1731-1754 (2003). Reviewer: Joaquín Jódar Reyes (Jaen) MSC: 17B37 17B67 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, Int. Math. Res. Not. 2003, No. 32, 1731--1754 (2003; Zbl 1080.17008) Full Text: DOI
Naito, Satoshi; Sagaki, Daisuke Three kinds of extremal weight vectors fixed by a diagram automorphism. (English) Zbl 1030.17004 J. Algebra 268, No. 1, 343-365 (2003). Reviewer: Stefano Capparelli (Roma) MSC: 17B10 17B37 PDFBibTeX XMLCite \textit{S. Naito} and \textit{D. Sagaki}, J. Algebra 268, No. 1, 343--365 (2003; Zbl 1030.17004) Full Text: DOI
Sagaki, Daisuke Crystal bases, path models, and a twining character formula for Demazure modules. (English) Zbl 1020.17017 Publ. Res. Inst. Math. Sci. 38, No. 2, 245-264 (2002). Reviewer: Robert Marsh (Leicester) MSC: 17B67 17B37 20G42 PDFBibTeX XMLCite \textit{D. Sagaki}, Publ. Res. Inst. Math. Sci. 38, No. 2, 245--264 (2002; Zbl 1020.17017) Full Text: DOI arXiv