On the generalized graded cellular bases for cyclotomic quiver Hecke-Clifford superalgebras

TL;DR

This paper constructs semisimple deformations and introduces generalized graded cellular superalgebras for cyclotomic quiver Hecke-Clifford superalgebras, unifying and extending known cellular results across multiple types.

Contribution

It develops a unified framework for generalized graded cellular structures in cyclotomic quiver Hecke-Clifford superalgebras, including new dimension formulas and deformation techniques.

Findings

Derived a unified dimension formula for bi-weight spaces.

Proved a large class of these superalgebras are generalized graded cellular.

Recovered known cellular results via idempotent truncation.

Abstract

In this paper, we construct semisimple deformations for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We derive a unified dimension formula for the bi-weight spaces for cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$. We introduce the notion of generalized graded cellular superalgebra. We prove a large class of cyclotomic quiver Hecke-Clifford superalgebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$, $A^{(2)}_{2s}$, $D^{(2)}_{s}$ is generalized graded cellular. By taking idempotent truncation, this recovers the known graded cellualr results for cyclotomic quiver Hecke algebras of types $A^{(1)}_{s-1}$, $C^{(1)}_{s}$.