Some multiplication formulas in queer $q$-Schur superalgebras
Jie Du, Haixia Gu, Zhenhua Li, Jinkui Wan

TL;DR
This paper derives explicit multiplication formulas in queer q-Schur superalgebras, advancing the understanding of their algebraic structure and setting the stage for new quantum supergroup realizations and duality applications.
Contribution
It provides explicit multiplication formulas for basis elements in queer q-Schur superalgebras, especially in the odd case, which was previously highly technical and complex.
Findings
Derived explicit multiplication formulas for basis elements.
Connected multiplication formulas to Hecke--Clifford algebra structures.
Laid groundwork for new quantum queer supergroup realizations.
Abstract
Building on the work [18], where some standard basis for the queer -Schur superalgebra is defined by a labelling set of matrices and their associated double coset representatives, we investigate the matrix representation of the regular module of with respect to this basis. More precisely, we derive explicitly (resp., partial explicitly) the multiplication formulas of the basis elements by certain even (resp., odd) generators of a queer -Schur superalgebra. These multiplication formulas are highly technical to derive, especially in the odd case. It requires to discover many multiplication (or commutation) formulas in the Hecke--Clifford algebra associated with the labelling matrices. For example, for a given such a labelling matrix , there are several matrices , , and…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra
