arXiv subjects

Zachary Carlini

Publications and source records attributed to Zachary Carlini.

2 recordsLinked to original sources

arXiv2023

Quasi-parabolic Kazhdan-Lusztig bases and reflection subgroups

Recently, Wang and the second author constructed a bar involution and canonical basis for a quasi-permutation module of the Hecke algebra associated to a type B Weyl group $W$, where the basis is parameterized by left cosets of a quasi-parabolic reflection subgroup in $W$. In this paper we provide an alternative approach to these constructions, and then generalize to Coxeter groups which contain a product of type B Weyl groups as a parabolic subgroup.

math.RT↗

arXiv2023

A new approach to the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups

We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups. The key to our approach is a new formula for the comultiplication of the $\imath$-divided powers, which allows us to reformulate the relations in terms of the adjoint action. We then obtain a proof using properties of the adjoint representation. The flexibility of this approach allows us to establish a more general family of relations which seem difficult to establish otherwise.

math.QA↗