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)

# An integral basis theorem for cyclotomic KLR algebras of type A

### Li

###### Speaker:

Ge Li (University of Sydney)

###### Title:

An integral basis theorem for cyclotomic KLR algebras of type A

###### Abstract:

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.

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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 John.Enyang@sydney.edu.au

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