Minimal polynomials and annihilators of generalized Verma modules of the scalar type

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dc.creatorOda, Hiroshi
dc.creatorOshima, Toshio
dc.date2004-10-31
dc.date2005-07-31
dc.date.accessioned2026-07-07T05:13:49Z
dc.date.available2026-07-07T05:13:49Z
dc.descriptionLet g be a complex reductive Lie algebra and U(g) the universal enveloping algebra of g. Associated to a faithful irreducible finite dimensional representation of g, a square matrix F with entries in U(g) naturally arises and if we consider the entries of F are elements in End(M) of a given U(g)-module M, the minimal polynomial of F is defined as the usual one for an associative algebra over the complex field. Suppose M is a generalized Verma module induced from a character of a parabolic subalgebra of g. In this paper a polynomial q(x) with the parameter of the character is constructed, which equals the minimal polynomial for the generic parameter. Then the two-sided ideal of U(g) generated by the entries of q(F) is studied. We give a sufficient condition for the parameter such that the ideal describes the difference of two left ideals related to M and the corresponding Verma module. The result has many applications. For example we can explicitly give a generator system of the annihilator of M for the generic parameter. This paper also deals with many concrete examples.
dc.description57 pages. v2: Accepted for publication in J. Lie Theory. Some details are changed to increase accessibility
dc.identifierhttps://arxiv.org/abs/math/0411006
dc.identifierhttp://arxiv.org/abs/math/0411006
dc.identifierJournal of Lie Theory 16 (2006), No. 1, 155-219
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73055
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject22E47; 16S30
dc.titleMinimal polynomials and annihilators of generalized Verma modules of the scalar type
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