Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U(gl(n))

2023/03/22 by Brini, Andrea, Teolis, Antonio
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.12412

Abstract

In this paper, we consider a special class of Capelli bitableaux, namely the Capelli-Deruyts bitableaux. The main results we prove are the hook coefficient lemma and the expansion theorem. Capelli-Deruyts bitableaux of rectangular shape are of particular interest since they are central elements in the enveloping algebra. The expansion theorem implies that these central element is explicitely described as a polynomial in the classical Capelli central elements. The hook coefficient lemma implies that the Capelli-Deruyts bitableaux are (canonically) expressed as the products of column determinants.

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