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Journal of Lie Theory 31 (2021), No. 4, 1141--1152
Copyright Heldermann Verlag 2021

Exponential Hilbert Series and Geometric Invariants of Flag Varieties

Wayne A. Johnson
Westminster College, Fulton, MO 65251, U.S.A.

We study properties of the exponential Hilbert series of a (partial) flag variety, G/P, where G is a semisimple, simply-connected complex linear algebraic group and P is a parabolic subgroup. We prove a relationship between the exponential Hilbert series and the degree and dimension of the flag variety. We then prove a combinatorial formula for the coefficients of an exponential analogue of the Hilbert polynomial. This formula is used in examples to prove further combinatorial identities involving Stirling numbers of the first and second kinds.

Keywords: Hilbert series, Stirling numbers, algebraic groups, representation theory.

MSC: 17B10

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