## View abstract

### Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Friday, July 16, 17:30 ~ 18:05 UTC-3

## Mixed perverse sheaves on flag varieties of Coxeter groups

### Cristian Vay

#### UNC & CONICET, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakc99bf4d1b3ab043d4d1c67ebdb51d37f').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc99bf4d1b3ab043d4d1c67ebdb51d37f = 'cr&#105;st&#105;&#97;n.v&#97;y' + '&#64;'; addyc99bf4d1b3ab043d4d1c67ebdb51d37f = addyc99bf4d1b3ab043d4d1c67ebdb51d37f + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r'; var addy_textc99bf4d1b3ab043d4d1c67ebdb51d37f = 'cr&#105;st&#105;&#97;n.v&#97;y' + '&#64;' + '&#117;nc' + '&#46;' + '&#101;d&#117;' + '&#46;' + '&#97;r';document.getElementById('cloakc99bf4d1b3ab043d4d1c67ebdb51d37f').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc99bf4d1b3ab043d4d1c67ebdb51d37f + '\'>'+addy_textc99bf4d1b3ab043d4d1c67ebdb51d37f+'<\/a>';

We construct an abelian category of mixed perverse sheaves'' attached to any realization of a Coxeter group, in terms of the associated Elias-Williamson diagrammatic category. This construction extends previous work of Achar and Riche, where they worked with parity complexes instead of diagrams, and we extend most of the properties known in this case to the general setting. As an application we prove that the split Grothendieck group of the Elias-Williamson diagrammatic category is isomorphic to the corresponding Hecke algebra, for any choice of realization.

Joint work with Pramod N. Achar (Louisiana State University, USA) and Simon Riche (Université Clermont Auvergne, France).