Nilpotency in type A cyclotomic quotients
Alexander E. Hoffnung
and Aaron D. Lauda
DOI: 10.1007/s10801-010-0226-8
Abstract
We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl( k).
Pages: 533–555
Keywords: keywords KLR algebra; categorification; cyclotomic quotient; tableau; Hecke algebra; anti-gravity
Full Text: PDF
References
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2. Brundan, J., Kleshchev, A.: Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras. Invent. Math. 178(3), 451-484 (2009).
3. Brundan, J., Kleshchev, A.: Graded decomposition numbers for cyclotomic Hecke algebras. Adv. Math. 222(6), 1883-1942 (2009)
4. Brundan, J., Kleshchev, A., Wang, W.: Graded Specht modules (2009).
5. Brundan, J., Stroppel, C.: Highest weight categories arising from Khovanov's diagram algebra III: category O (2008).
6. Hu, J., Mathas, A.: Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009).
7. Khovanov, M., Lauda, A.: A diagrammatic approach to categorification of quantum groups II. Trans. Am. Math. Soc. (2008, to appear)
8. Khovanov, M., Lauda, A.: A diagrammatic approach to categorification of quantum groups III. Quantum Topology 1(1), 1-92 (2010)
9. Khovanov, M., Lauda, A.: A diagrammatic approach to categorification of quantum groups I. Represent. Theory 13, 309-347 (2009). [math.QA]
10. Kleshchev, A., Ram, A.: Homogeneous representations of Khovanov-Lauda algebras (2008).
11. Rouquier, R.: 2-Kac-Moody algebras (2008).
12. Viennot, G.: Heaps of pieces. I. Basic definitions and combinatorial lemmas. In: Combinatoire énumérative, Montreal, Que., 1985/Quebec, Que.,
1985. Lecture Notes in Math., vol. 1234, pp. 321-
350. Springer, Berlin (1986)
13. Varagnolo, M., Vasserot, E.: Canonical bases and Khovanov-Lauda algebras (2009).
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