Comet Calendar
Algebra and Combinatorics Seminar
Wednesday, October 19, 2022 11:30am to 12:30pm
Event Details
Speaker: Dillon Hanson (University of North Texas)
Title: Invariant Theory of Modular Reflection Groups
Abstract: We consider finite reflection groups acting over fields of arbitrary characteristic. Many arguments of classical invariant theory break down in the modular setting, when the characteristic of the field divides the order of the group. Here, we examine the action on differential derivations, which arise in Catalan combinatorics. We develop an analogue of Saito’s freeness criterion that distinguishes the characteristic 2 case and obtain an explicit description of the invariant differential derivations for special linear groups and general linear groups over finite fields.
Abstract: We consider finite reflection groups acting over fields of arbitrary characteristic. Many arguments of classical invariant theory break down in the modular setting, when the characteristic of the field divides the order of the group. Here, we examine the action on differential derivations, which arise in Catalan combinatorics. We develop an analogue of Saito’s freeness criterion that distinguishes the characteristic 2 case and obtain an explicit description of the invariant differential derivations for special linear groups and general linear groups over finite fields.
Location
Cecil H. Green Hall (GR), 4.204
800 W. Campbell Road, Richardson, Texas 75080-3021
Department
- Natural Sciences & Mathematics
Contact Information
- Nathan Williams
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