Original scientific paper

https://doi.org/10.21857/y26kecg7e9

Weird K-actions on U(g) for so(n,1) and su(n,1)

Hrvoje Kraljević orcid.org/0000-0002-8328-0815 ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

Abstract

Let g0 be either so(n, 1) or su(n, 1), g its complexification, K a maximal compact subgroup of the adjoint group of g0, U(g) the universal enveloping algebra of g and U(g)K its subalgebra of K-invariants. A consequence of our results in [2] is that besides the usual adjoint action of K on U(g) there is another action of K commuting with the adjoint action and leaving U(g)K pointwise invariant. The case g0 = so(2, 1) ≃ su(1, 1) is trivial since K is commutative and the weird action of K coincides with the inverse of adjoint action. We investigate closely the weird action of K in the simplest nontrivial case g0 = so(3, 1).

Keywords

Universal enveloping algebra; K-types; adjoint action; K-invariants; K-harmonic polynomials

Hrčak ID:

313633

URI

https://hrcak.srce.hr/313633

Publication date:

24.1.2024.

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