Hsiao, Chin-Yu; Ma, Xiaonan; Marinescu, George Geometric quantization on CR manifolds. (English) Zbl 07741153 Commun. Contemp. Math. 25, No. 10, Article ID 2250074, 73 p. (2023). Reviewer: Huan Wang (Zhengzhou) MSC: 53D50 53D20 32W10 32L10 35S30 32V20 PDFBibTeX XMLCite \textit{C.-Y. Hsiao} et al., Commun. Contemp. Math. 25, No. 10, Article ID 2250074, 73 p. (2023; Zbl 07741153) Full Text: DOI arXiv
Fujita, Hajime Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds. (English) Zbl 1493.19005 Can. J. Math. 74, No. 4, 1062-1092 (2022). Reviewer: Iakovos Androulidakis (Athína) MSC: 19K56 53D50 57S25 58J22 PDFBibTeX XMLCite \textit{H. Fujita}, Can. J. Math. 74, No. 4, 1062--1092 (2022; Zbl 1493.19005) Full Text: DOI arXiv
Huang, Rung-Tzung; Shao, Guokuan Asymptotics of G-equivariant Szegő kernels. (English) Zbl 1495.32095 Ann. Global Anal. Geom. 61, No. 4, 869-893 (2022). MSC: 32V20 PDFBibTeX XMLCite \textit{R.-T. Huang} and \textit{G. Shao}, Ann. Global Anal. Geom. 61, No. 4, 869--893 (2022; Zbl 1495.32095) Full Text: DOI arXiv
Ma, Xiaonan Quantization commutes with reduction, a survey. (English) Zbl 1513.58014 Acta Math. Sci., Ser. B, Engl. Ed. 41, No. 6, 1859-1872 (2021). MSC: 58J20 53D50 32V10 PDFBibTeX XMLCite \textit{X. Ma}, Acta Math. Sci., Ser. B, Engl. Ed. 41, No. 6, 1859--1872 (2021; Zbl 1513.58014) Full Text: DOI
Guillemin, Victor W.; Miranda, Eva; Weitsman, Jonathan On geometric quantization of \(b^m\)-symplectic manifolds. (English) Zbl 1465.81057 Math. Z. 298, No. 1-2, 281-288 (2021). MSC: 81S10 53D50 53D17 70H05 14M25 11F11 PDFBibTeX XMLCite \textit{V. W. Guillemin} et al., Math. Z. 298, No. 1--2, 281--288 (2021; Zbl 1465.81057) Full Text: DOI arXiv
Rousseva, Jenia; Uribe, Alejandro Reduction and coherent states. (English) Zbl 1472.81101 Lett. Math. Phys. 111, No. 2, Paper No. 52, 44 p. (2021). Reviewer: Alex B. Gaina (Chişinău) MSC: 81Q20 81R30 81R25 81T33 35S30 PDFBibTeX XMLCite \textit{J. Rousseva} and \textit{A. Uribe}, Lett. Math. Phys. 111, No. 2, Paper No. 52, 44 p. (2021; Zbl 1472.81101) Full Text: DOI arXiv
Hsiao, Chin-Yu; Huang, Rung-Tzung \(G\)-invariant Szegő kernel asymptotics and CR reduction. (English) Zbl 1467.32016 Calc. Var. Partial Differ. Equ. 60, No. 1, Paper No. 47, 49 p. (2021). Reviewer: Emil J. Straube (College Station) MSC: 32V20 PDFBibTeX XMLCite \textit{C.-Y. Hsiao} and \textit{R.-T. Huang}, Calc. Var. Partial Differ. Equ. 60, No. 1, Paper No. 47, 49 p. (2021; Zbl 1467.32016) Full Text: DOI arXiv
Loizides, Yiannis; Rodsphon, Rudy; Song, Yanli A \(KK\)-theoretic perspective on deformed Dirac operators. (English) Zbl 1457.19009 Adv. Math. 380, Article ID 107604, 35 p. (2021). Reviewer: Iakovos Androulidakis (Athína) MSC: 19K56 58J20 53D50 46L80 PDFBibTeX XMLCite \textit{Y. Loizides} et al., Adv. Math. 380, Article ID 107604, 35 p. (2021; Zbl 1457.19009) Full Text: DOI arXiv
Loizides, Yiannis; Paradan, Paul-Emile; Vergne, Michele Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization. (English) Zbl 1459.58007 Indag. Math., New Ser. 32, No. 1, 151-192 (2021). Reviewer: Gabor Etesi (Budapest) MSC: 58J20 52C07 53D50 53D20 PDFBibTeX XMLCite \textit{Y. Loizides} et al., Indag. Math., New Ser. 32, No. 1, 151--192 (2021; Zbl 1459.58007) Full Text: DOI arXiv
Hochs, Peter; Song, Yanli; Yu, Shilin A geometric realisation of tempered representations restricted to maximal compact subgroups. (English) Zbl 1454.22011 Math. Ann. 378, No. 1-2, 97-152 (2020). Reviewer: Jorge Vargas (Córdoba) MSC: 22E47 22E60 53D50 PDFBibTeX XMLCite \textit{P. Hochs} et al., Math. Ann. 378, No. 1--2, 97--152 (2020; Zbl 1454.22011) Full Text: DOI arXiv
Loizides, Yiannis; Song, Yanli Norm-square localization and the quantization of Hamiltonian loop group spaces. (English) Zbl 1433.58021 J. Funct. Anal. 278, No. 9, Article ID 108445, 45 p. (2020). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 58J20 53D50 58J32 53D20 PDFBibTeX XMLCite \textit{Y. Loizides} and \textit{Y. Song}, J. Funct. Anal. 278, No. 9, Article ID 108445, 45 p. (2020; Zbl 1433.58021) Full Text: DOI arXiv
Paradan, Paul-Emile Kirillov’s orbit method: the case of discrete series representations. (English) Zbl 1431.22014 Duke Math. J. 168, No. 16, 3103-3134 (2019). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 22E46 53C27 58J20 PDFBibTeX XMLCite \textit{P.-E. Paradan}, Duke Math. J. 168, No. 16, 3103--3134 (2019; Zbl 1431.22014) Full Text: DOI arXiv
Boeijink, Jord; Landsman, Klaas; van Suijlekom, Walter Quantization commutes with singular reduction: cotangent bundles of compact Lie groups. (English) Zbl 1431.53097 Rev. Math. Phys. 31, No. 6, Article ID 1950016, 45 p. (2019). MSC: 53D50 81S10 PDFBibTeX XMLCite \textit{J. Boeijink} et al., Rev. Math. Phys. 31, No. 6, Article ID 1950016, 45 p. (2019; Zbl 1431.53097) Full Text: DOI arXiv
Hochs, Peter; Song, Yanli; Yu, Shilin A geometric formula for multiplicities of \(K\)-types of tempered representations. (English) Zbl 1429.22015 Trans. Am. Math. Soc. 372, No. 12, 8553-8586 (2019). Reviewer: Andrew Bucki (Edmond) MSC: 22E46 53D50 53D20 53C27 58J20 PDFBibTeX XMLCite \textit{P. Hochs} et al., Trans. Am. Math. Soc. 372, No. 12, 8553--8586 (2019; Zbl 1429.22015) Full Text: DOI arXiv
Paradan, Paul-Emile; Vergne, Michèle Witten non abelian localization for equivariant \(K\)-theory, and the \([Q,R]=0\) theorem. (English) Zbl 1439.58015 Memoirs of the American Mathematical Society 1257. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3522-6/pbk; 978-1-4704-5397-8/ebook). v, 71 p. (2019). Reviewer: Tatsuki Seto (Tokyo) MSC: 58J20 53D50 53C27 19K56 57S15 32Q60 PDFBibTeX XMLCite \textit{P.-E. Paradan} and \textit{M. Vergne}, Witten non abelian localization for equivariant \(K\)-theory, and the \([Q,R]=0\) theorem. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1439.58015) Full Text: DOI arXiv
Paradan, Paul-Emile Formal geometric quantization. III: Functoriality in the \(\mathrm{spin}^c\) setting. (English) Zbl 1403.53078 Algebr. Represent. Theory 21, No. 5, 1151-1164 (2018). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 53D50 57S15 53C27 58J20 PDFBibTeX XMLCite \textit{P.-E. Paradan}, Algebr. Represent. Theory 21, No. 5, 1151--1164 (2018; Zbl 1403.53078) Full Text: DOI arXiv
Hochs, Peter; Wang, Hang A fixed point theorem on noncompact manifolds. (English) Zbl 1401.58010 Ann. \(K\)-Theory 3, No. 2, 235-286 (2018). Reviewer: Karsten Bohlen (Regensburg) MSC: 58J20 19K35 22E46 58C30 PDFBibTeX XMLCite \textit{P. Hochs} and \textit{H. Wang}, Ann. \(K\)-Theory 3, No. 2, 235--286 (2018; Zbl 1401.58010) Full Text: DOI arXiv
Wang, Xiangsheng Elliptic boundary value problem on non-compact \(G\)-manifolds. (English) Zbl 1430.58017 Int. J. Math. 28, No. 4, Article ID 1750025, 35 p. (2017). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 58J20 58J32 53D50 53C27 PDFBibTeX XMLCite \textit{X. Wang}, Int. J. Math. 28, No. 4, Article ID 1750025, 35 p. (2017; Zbl 1430.58017) Full Text: DOI arXiv
Vergne, Michèle The equivariant Riemann-Roch theorem and the graded Todd class. (Le théorème de Riemann-Roch équivariant et la classe de Todd graduée.) (English. French summary) Zbl 1414.53081 C. R., Math., Acad. Sci. Paris 355, No. 5, 563-570 (2017). MSC: 53D50 53D05 53D20 81S10 PDFBibTeX XMLCite \textit{M. Vergne}, C. R., Math., Acad. Sci. Paris 355, No. 5, 563--570 (2017; Zbl 1414.53081) Full Text: DOI arXiv
Hochs, Peter; Song, Yanli On the Vergne conjecture. (English) Zbl 1364.53089 Arch. Math. 108, No. 1, 99-112 (2017). Reviewer: Benjamin Cahen (Metz) MSC: 53D50 58J20 53D20 PDFBibTeX XMLCite \textit{P. Hochs} and \textit{Y. Song}, Arch. Math. 108, No. 1, 99--112 (2017; Zbl 1364.53089) Full Text: DOI arXiv
Song, Yanli A \(K\)-homological approach to the quantization commutes with reduction problem. (English) Zbl 1360.53086 J. Geom. Phys. 112, 29-44 (2017). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 53D20 53D50 81Q05 58A12 PDFBibTeX XMLCite \textit{Y. Song}, J. Geom. Phys. 112, 29--44 (2017; Zbl 1360.53086) Full Text: DOI arXiv
Hochs, Peter; Song, Yanli An equivariant index for proper actions. I. (English) Zbl 1353.58011 J. Funct. Anal. 272, No. 2, 661-704 (2017). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 58J22 46L05 PDFBibTeX XMLCite \textit{P. Hochs} and \textit{Y. Song}, J. Funct. Anal. 272, No. 2, 661--704 (2017; Zbl 1353.58011) Full Text: DOI arXiv
Hochs, Peter; Mathai, Varghese Formal geometric quantisation for proper actions. (English) Zbl 1353.53092 J. Homotopy Relat. Struct. 11, No. 3, 409-424 (2016). Reviewer: Andrew Bucki (Edmond) MSC: 53D50 22D15 22E46 PDFBibTeX XMLCite \textit{P. Hochs} and \textit{V. Mathai}, J. Homotopy Relat. Struct. 11, No. 3, 409--424 (2016; Zbl 1353.53092) Full Text: DOI arXiv
Hochs, Peter; Mathai, Varghese Geometric quantization and families of inner products. (English) Zbl 1325.53115 Adv. Math. 282, 362-426 (2015). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 53D50 81S10 53C27 53D20 58J20 PDFBibTeX XMLCite \textit{P. Hochs} and \textit{V. Mathai}, Adv. Math. 282, 362--426 (2015; Zbl 1325.53115) Full Text: DOI arXiv
Paradan, Paul-Emile Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series. (English) Zbl 1355.53074 J. Eur. Math. Soc. (JEMS) 17, No. 4, 955-990 (2015). MSC: 53D50 57S15 17B08 22E46 53D20 PDFBibTeX XMLCite \textit{P.-E. Paradan}, J. Eur. Math. Soc. (JEMS) 17, No. 4, 955--990 (2015; Zbl 1355.53074) Full Text: DOI arXiv
Hochs, Peter Quantisation of presymplectic manifolds, \(K\)-theory and group representations. (English) Zbl 1320.53110 Proc. Am. Math. Soc. 143, No. 6, 2675-2692 (2015). MSC: 53D50 19K56 22D25 PDFBibTeX XMLCite \textit{P. Hochs}, Proc. Am. Math. Soc. 143, No. 6, 2675--2692 (2015; Zbl 1320.53110) Full Text: DOI arXiv
Braverman, Maxim Background cohomology of a non-compact Kähler \(G\)-manifold. (English) Zbl 1307.32016 Trans. Am. Math. Soc. 367, No. 3, 2235-2262 (2015). MSC: 32L10 PDFBibTeX XMLCite \textit{M. Braverman}, Trans. Am. Math. Soc. 367, No. 3, 2235--2262 (2015; Zbl 1307.32016) Full Text: DOI arXiv
Ma, Xiaonan; Zhang, Weiping Geometric quantization for proper moment maps: the Vergne conjecture. (English) Zbl 1380.53102 Acta Math. 212, No. 1, 11-57 (2014). MSC: 53D50 53D20 57S99 PDFBibTeX XMLCite \textit{X. Ma} and \textit{W. Zhang}, Acta Math. 212, No. 1, 11--57 (2014; Zbl 1380.53102) Full Text: DOI arXiv