CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Generalized (q)-Schur algebras and their quasihereditary structure Steve Doty, Loyola University Chicago
February 5 and 12, 2013 Math 350 2-3pm	Abstract Generalized Schur algebras were introduced in the late 1980s by S. Donkin. They are one way of extending the classical theory from Type A root systems to arbitrary type, and of course q-analogues exist. In 2002 Giaquinto and I found two presentations of the classical Schur algebras and their q-analogues; one of them generalized to arbitrary type. One of the most important facts about generalized q-Schur algebras is that they are quasihereditary (in the sense of Cline-Parshall-Scott). I proved this in 2003 as an application of known facts about the Lusztig-Kashiwara canonical-crystal bases for quantized enveloping algebras of semisimple Lie algebras. Recently, Giaquinto and I found an elementary proof that does not depend on the deep existence results of Lusztig and Kashiwara. Instead, the proof starts from the defining presentation and uses only known results on Lie algebras and elementary calculations.

Generalized (q)-Schur algebras and their quasihereditary structure

Steve Doty, Loyola University Chicago

February 5 and 12, 2013

Math 350

2-3pm

Abstract

Generalized Schur algebras were introduced in the late 1980s by S. Donkin. They are one way of extending the classical theory from Type A root systems to arbitrary type, and of course q-analogues exist. In 2002 Giaquinto and I found two presentations of the classical Schur algebras and their q-analogues; one of them generalized to arbitrary type.

One of the most important facts about generalized q-Schur algebras is that they are quasihereditary (in the sense of Cline-Parshall-Scott). I proved this in 2003 as an application of known facts about the Lusztig-Kashiwara canonical-crystal bases for quantized enveloping algebras of semisimple Lie algebras. Recently, Giaquinto and I found an elementary proof that does not depend on the deep existence results of Lusztig and Kashiwara. Instead, the proof starts from the defining presentation and uses only known results on Lie algebras and elementary calculations.