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 are 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.

Andrea Brini (2023). Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U(gl(n)). COMMUNICATIONS IN ALGEBRA, 51(10), 4113-4149 [10.1080/00927872.2023.2197072].

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

Andrea Brini
2023

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 are 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.
2023
Andrea Brini (2023). Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U(gl(n)). COMMUNICATIONS IN ALGEBRA, 51(10), 4113-4149 [10.1080/00927872.2023.2197072].
Andrea Brini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/921594
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