Upper estimates of the Morse numbers for the matrix elements of real linear irreducible representations of compact connected simple Lie groups. (English. Russian original) Zbl 1521.22010
St. Petersbg. Math. J. 33, No. 6, 971-980 (2022); translation from Algebra Anal. 33, No. 6, 107-120 (2021).
Summary: The Morse numbers of spaces of matrix elements for real irreducible linear representations of compact connected simple Lie groups are estimate from above in a variety of ways, in terms of the dimension, the Dynkin index of the representation, the eigenvalues of the invariant Laplace operator, and the volume of the group.
MSC:
| 22E45 | Representations of Lie and linear algebraic groups over real fields: analytic methods |
Keywords:
compact connected simple Lie group; real irreducible linear representation; matrix elements; Morse numbers; spectrum of Laplace operator; volume of groupReferences:
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