Abstract: Bounded symmetric domains D=G/K are an important class of multivariable pseudo-convex domains, with close connection to representation theory of semi-simple Lie groups G and the theory of automorphic forms. We study Toeplitz operators on Hilbert spaces of holomorphic functions on D, the so-called weighted Bergman spaces, and present two recent results:
(i) Eigenvalue formulas for K-invariant Toeplitz operators, where K is the maximal compact subgroup of G, using the theory of Schur functions and partitions.
(ii) A stratification of the eigenspace bundle for K-invariant Hilbert modules, which have singularities given by determinantal varieties. The talk will include some introduction to the Jordan algebraic description of bounded symmetric domains.
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