Transactions of the American Mathematical Society

Author(s): Riccardo Biagioli
Journal: Trans. Amer. Math. Soc. 356 (2004), 159-184.
MSC (2000): Primary 17B10, 05E99; Secondary 22E47, 20F55
Posted: August 26, 2003
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Abstract: We give explicit combinatorial product formulas for the polynomials encoding the dimensions of the spaces of extensions of

-generalized Verma modules, in the cases when

corresponds to an indecomposable classic Hermitian symmetric pair. The formulas imply that these dimensions are combinatorial invariants. We also discuss how these polynomials, defined by Shelton, are related to the parabolic

-polynomials introduced by Deodhar.

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