Zubov, Dmitriĭ I. Projections of orbital measures for classical Lie groups. (English. Russian original) Zbl 1360.22025 Funct. Anal. Appl. 50, No. 3, 228-232 (2016); translation from Funkts. Anal. Prilozh. 50, No. 3, 76-81 (2016). Let \(G_n\) be one of the compact groups \(\mathrm{SO}(2n+1)\), \(\mathrm{Sp}(2n)\) or \(\mathrm{SO}(2n)\). Let \(g_n\) be the corresponding Lie algebra. Each orbit \(X\) of an adjoint action of \(G_n\) onto \(g_n\) carries a unique invariant probability measure \(\mu_X\). The set of all orbits is denoted by \(X_n\).Take a natural projection \(p_n^k:g_n\rightarrow g_k\), \(k<n\). The projection of \(\mu_X\) can be represented as a continuous combination of orbital measures in the following manner \[ p_n^k(\mu_X)(S)=\int_{Y\in X_k} \mu_Y(S) \nu_{X, k}(dY), \]where \(\nu_{X, k}(dY)\) is a certain probability measure on \(X_n\).The main result of the paper is an explicit formula for \(\nu_{X, k}(dY)\).The case of \(U(n)\) was considered in [G. Olshanski, J. Lie Theory 23, No. 4, 1011–1022 (2013; Zbl 1281.22003)] and [J. Faraut, Adv. Pure Appl. Math. 6, No. 4, 261–283 (2015; Zbl 1326.15058)]. Reviewer: Dmitry Artamonov (Moskva) Cited in 3 Documents MSC: 22E60 Lie algebras of Lie groups Keywords:orbital measures; B-splines; divided differences; Harish-Chandra-Itzykson-Zuber integral Citations:Zbl 1281.22003; Zbl 1326.15058 PDFBibTeX XMLCite \textit{D. I. Zubov}, Funct. Anal. Appl. 50, No. 3, 228--232 (2016; Zbl 1360.22025); translation from Funkts. Anal. Prilozh. 50, No. 3, 76--81 (2016) Full Text: DOI arXiv References: [1] Curry, H. B.; Schoenberg, I. J., No article title, J. Anal. Math., 17, 71-107 (1966) · Zbl 0146.08404 · doi:10.1007/BF02788653 [2] Faraut, J., No article title, Adv. Pure Appl. Math., 6, 261-283 (2015) · Zbl 1326.15058 · doi:10.1515/apam-2015-5012 [3] Harish-Chandra, No article title, Amer. J. Math., 79, 87-120 (1957) · Zbl 0072.01901 · doi:10.2307/2372387 [4] Olshanski, G., No article title, J. Lie Theory, 23, 1011-1022 (2013) · Zbl 1281.22003 [5] G. M. Phillips, Interpolation and approximation by polynomials, CMS Books in Math, vol. 14, Springer-Verlag, New York, 2003. · Zbl 1023.41002 · doi:10.1007/b97417 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.