Type: Seminar

Distribution: World

Auth: afish@p617.pc (assumed)

Speaker: Dr. Anthony Licata http://maths-people.anu.edu.au/~licatat/Anthony_Licata_homepage/Home.html Time: Friday, May 3, 2:00--3:00PM Room: Room: RC-4082, Red Centre (UNSW) ----------------------------------------------- Title: Positivity and integrality from higher representation theory Abstract: One of the important consequences of the geometric methods introduced in representation theory over the last thirty years has been the discovery that representations of important algebras in Lie theory often have natural - or "canonical" bases; when written in these bases, the representation theory of the algebra can be formulated over the positive integers, instead of, say, over the complex numbers. One byproduct of such positive integrality is that a wealth of combinatorics emerges. Of course, proving these various positivity and integrality statements is sometimes hard work. In this talk we will explain how ideas from "higher representation theory" can be used to prove positivity and integrality statements. In particular, we will explain some of the mathematics behind the recent proof by Elias-Williamson of the positivity of Kazdhan-Lusztig polynomials in the representation theory of the Hecke algebra. ----------------------------------------------- Lunch with speaker: we meet around 12:30PM at the entrance to the East Wing of Red Centre Building. One choice of commuting from Sydney: meet at Carslaw 620 around 12:05PM and share taxi to UNSW. The round trip is covered by department colloquium fund. Joint Colloquium web site: http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html