An integral basis theorem for cyclotomic KLR algebras of type A

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

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 $R_n^{\mathrm{\Lambda }}$ are isomorphic to the cyclotomic Hecke algebras of type $A$, $H_n^{\mathrm{\Lambda }}$ 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 $R_n^{\mathrm{\Lambda }}$ 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