On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras

2025/11/23 by Li, Shuo, Shi, Lei
Mathematics · #16G99 #16W55 #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.18395

openalex publication_date 2025/11/23 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra H^f_c(n) is supersymmetric if f=f^(\mathtt0)_\underlineQ and, symmetric if f=f^(\mathtts)_\underlineQ and an invertibility condition holds. In the semisimple case, we compute the Schur elements for both H^f_c(n) and the cyclotomic Sergeev algebra h^g_c(n). As applications, we define new symmetrizing forms on the Hecke-Clifford algebra H(n) and on the cyclotomic quiver Hecke algebras of types A⁽¹⁾_e-1 and C⁽¹⁾_e.

Related

• On representation theory of cyclotomic Hecke-Clifford algebras
• Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras
• Cyclotomic q-Schur superalgebras
• Multiplication formulas and isomorphism theorem of \imathSchur superalgebras
• A super Frobenius formula for the characters of cyclotomic Hecke algebras