Fused permutations algebras and degenerate affine Hecke algebras

TL;DR

This paper introduces the fused permutations algebra as a quotient of the degenerate cyclotomic affine Hecke algebra, providing a basis description and analyzing primitive idempotents to deepen algebraic understanding.

Contribution

It presents an algebraic presentation of the fused permutations algebra and establishes its relationship as a quotient of the degenerate cyclotomic affine Hecke algebra, including a combinatorial basis.

Findings

Fused permutations algebra is a quotient of the degenerate cyclotomic affine Hecke algebra.

A combinatorial basis is described using signed permutations with pattern avoidance.

Primitive idempotents of the algebra are characterized and studied.

Abstract

This paper gives an algebraic presentation of an algebra called the fused permutations algebra in the one-boundary case. It is obtained through a detailed study of the degenerate cyclotomic Hecke algebra. In particular, we prove that the fused permutations algebra is a quotient of the degenerate cyclotomic affine Hecke algebra, and we also describe a basis combinatorially in terms of signed permutations with avoiding patterns. In order to understand this quotient, we study the primitive idempotents of this degenerate cyclotomic affine Hecke algebra.