Exponential Hilbert series of equivariant embeddings

2018/04/13 by Wayne A. Johnson, Johnson, Wayne A.
Mathematics · #17B10 #20G05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.04943

openalex publication_date 2018/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study properties of the exponential Hilbert series of a G-equivariant projective variety, where G is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities involving Stirling numbers of the first and second kinds.

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