Algebra Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
18 May 2021
14:15
Alistair Savage
Abstract

The elliptic Hall algebra has appeared in many different contexts in representation theory and geometry under different names.  We will explain how this algebra is categorified by the quantum Heisenberg category.  This diagrammatic category is modelled on affine Hecke algebras and can be viewed as a deformation of the framed HOMFLYPT skein category underpinning the HOMFLYPT link invariant.  Using the categorification of the elliptic Hall algebra, one can construct large families of representations for this algebra.

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1 June 2021
14:15
Chris Bowman
Abstract

Riche—Williamson recently proved that the characters of tilting modules for GL_h are given by non-singular p-Kazhdan—Lusztig polynomials providing p>h.  This is equivalent to calculating the decomposition numbers for symmetric groups labelled by partitions with at most h columns.  We discuss how this result can be generalised to all cyclotomic quiver Hecke algebras via a new and explicit isomorphism between (truncations of) quiver Hecke algebras and Elias–Williamson’s diagrammatic endomorphism algebras of Bott–Samelson bimodules. 

This allows us to give an elementary and explicit proof of the main theorem of Riche–Williamson’s recent monograph and extend their categorical equivalence to all cyclotomic quiver Hecke algebras, thus solving Libedinsky–Plaza’s categorical blob conjecture.  Furthermore, it allows us to classify and construct the homogeneous simple modules of quiver Hecke algebras via BGG resolutions.   
 
This is joint work with A. Cox, A. Hazi, D.Michailidis, E. Norton, and J. Simental.  
 

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