Higher-level degenerate spin affine Hecke superalgebras

2026/07/30 by Thomas Moran
Mathematics · #math.RT #msc:20C08 #msc:18M30 #msc:18M05

paper · pdf

27 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We define a new class of superalgebras, called higher-level degenerate spin affine Hecke superalgebras, and study their structure theory. We establish an isomorphism that relates the higher-level degenerate spin affine Hecke superalgebras to the higher-level degenerate affine Hecke-Clifford superalgebras. The relationship between these superalgebras is a higher-level analogue of the relationship between the degenerate spin affine Hecke superalgebras and degenerate affine Hecke-Clifford superalgebras.

Citations

• RoCK blocks for double covers of symmetric groups and quiver Hecke superalgebras
• Presentations of linear monoidal categories and their endomorphism algebras
• Higher level affine Schur and Hecke algebras
• Quiver Hecke superalgebras
• Hecke-Clifford superalgebras, crystals of type A_2l⁽²⁾ and modular branching rules for S_n
• Affine Sergeev Algebra and q-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group

Related

• Degenerate Affine Hecke-Clifford Algebras and Type Q Lie Superalgebras
• Hecke-Clifford algebras and spin Hecke algebras III: the trigonometric type
• Quiver Hecke superalgebras
• Higher level affine Schur and Hecke algebras
• Degenerate Double Affine Hecke Algebra And Conformal Field Theory