Deformations of unitary Howe dual pairs

2020/09/11 by Dan Ciubotaru, Hendrik De Bie, Ciubotaru, Dan +5 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2009.05412

Abstract

We study deformations of the Howe dual pairs (U(n),\mathfraku(1,1)) and (U(n),\mathfraku(2|1)) to the context of a rational Cherednik algebra H_1,c(G,E) associated with a real reflection group G acting on a real vector space E of even dimension. For each pair, we show that the Lie (super)algebra structure of one partner is preserved under the deformation, which leads to a multiplicity-free decomposition of the standard module or its tensor product with a spinor space. For the case where E is two-dimensional and G is a dihedral group, we provide complete descriptions for the deformed pair and the relevant joint-decomposition.

Citations

• Differential-difference operators associated to reflection groups

Cited by

• The double dihedral Dunkl total angular momentum algebra
• On angular momentum algebras and their relations

Related

• The Dunkl-Cherednik Deformation of a Howe duality
• The double dihedral Dunkl total angular momentum algebra
• Quantum Howe duality and invariant polynomials
• Deformations of Quantum Symmetric Algebras Extended by Groups
• Symmetry breaking operators for dual pairs with one member compact