A new approach to computing generators for U (g)K

Steven Glenn Jackson; Alfred G. Noël

doi:10.1016/j.jalgebra.2009.07.004

A new approach to computing generators for U (g)^K

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (G, K) be the complex symmetric pair associated with a real reductive Lie group G₀. We discuss an algorithmic approach to computing generators for the centralizer of K in the universal enveloping algebra of g. In particular, we compute explicit generators for the cases G₀ = SU (2, 2), SL (3, R), SL (4, R), Sp (4, R), and the exceptional group G_{2 (2)}.

Original language	English
Pages (from-to)	2607-2620
Number of pages	14
Journal	Journal of Algebra
Volume	322
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2009.07.004
State	Published - Oct 15 2009

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Centralizer of a maximal compact subgroup
Semisimple Lie group
Universal enveloping algebra

Access to Document

10.1016/j.jalgebra.2009.07.004

Cite this

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abstract = "Let (G, K) be the complex symmetric pair associated with a real reductive Lie group G0. We discuss an algorithmic approach to computing generators for the centralizer of K in the universal enveloping algebra of g. In particular, we compute explicit generators for the cases G0 = SU (2, 2), SL (3, R), SL (4, R), Sp (4, R), and the exceptional group G2 (2).",

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AB - Let (G, K) be the complex symmetric pair associated with a real reductive Lie group G0. We discuss an algorithmic approach to computing generators for the centralizer of K in the universal enveloping algebra of g. In particular, we compute explicit generators for the cases G0 = SU (2, 2), SL (3, R), SL (4, R), Sp (4, R), and the exceptional group G2 (2).

KW - Centralizer of a maximal compact subgroup

KW - Semisimple Lie group

KW - Universal enveloping algebra

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