SMS scnews item created by John Enyang at Tue 13 Nov 2012 0932
Type: Seminar
Distribution: World
Expiry: 17 Nov 2012
Calendar1: 16 Nov 2012 1205-1255
CalLoc1: Carslaw 173
Auth: enyang@penyang.pc (assumed)

Algebra Seminar

An integral basis theorem for cyclotomic KLR algebras of type A


Friday 16th November, 12:05--12:55pm, Carslaw 173


Ge Li (University of Sydney)


An integral basis theorem for cyclotomic KLR algebras of type A


Khovanov and Lauda and Rouquier have introduced a remarkable new family of algebras \(R_n\), the quiver Hecke algebras, for each oriented quiver. The algebras \(R_n\) are naturally \(\mathbb{Z}\)-graded. Brundan and Kleshchev proved that over a field \(F\), the cyclotomic Khovanov-Lauda-Rouquier algebras \(R_n^\Lambda\) are isomorphic to the cyclotomic Hecke algebras of type \(A\), \(H_n^\Lambda\) by constructing an explicit isomorphic mapping, which gives a \(\mathbb{Z}\)-grading to the cyclotomic Hecke algebras. Based on Brundan and Kleshchev's work, Hu and Mathas constructed a graded cellular basis with some restriction. In this talk I will show that such restriction can be removed and the graded cellular basis introduced by Hu and Mathas can be extended to \(R_n^\Lambda\) over \(\mathbb{Z}\). Furthermore we will show that the graded cellular basis can be extended to affine Khovanov-Lauda-Rouquier algebras and it gives a classification of all simple \(R_n\)-modules.


After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang

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