Completely splittable representations of affine Hecke-Clifford algebras
Jinkui Wan
DOI: 10.1007/s10801-009-0202-3
Abstract
We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.
Pages: 15–58
Keywords: keywords completely splittable; affine Hecke-Clifford algebra
Full Text: PDF
References
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9. Kleshchev, A., Ram, A.: Homogeneous representations of Khovanov-Lauda algebras. (2008)
10. Leclerc, B.: Dual canonical bases, quantum shuffles and q-characters. Math. Z. 246(4), 691-732 (2004)
11. Lusztig, G.: Affine Hecke algebras and their graded version. J. Amer. Math. Soc. 2, 599-635 (1989)
12. Mathieu, O.: On the dimension of some modular irreducible representations of the symmetric group. Lett. Math. Phys. 38, 23-32 (1996)
13. Nazarov, M.: Young's orthogonal form of irreducible projective representations of the symmetric group. J. London Math. Soc. (2) 42(3), 437-451 (1990)
14. Nazarov, M.: Young's symmetrizers for projective representations of the symmetric group. Adv. Math. 127(2), 190-257 (1997)
15. Okounkov, A., Vershik, A.: A new approach to representation theory of symmetric groups. Selecta Math. (N.S.) 2, 581-605 (1996) J Algebr Comb (2010) 32: 15-58
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1. Brundan, J., Kleshchev, A.: Hecke-Clifford superalgebras, crystals of type A , and modular branch- 2l ing rules for Sn. Repr. Theory 5, 317-403 (2001)
2. Cherednik, I.: Special bases of irreducible representations of a degenerate affine Hecke algebra. Funct. Anal. Appl. 20(1), 76-78 (1986)
3. Cherednik, I.: A new interpretation of Gel'fand-Tzetlin bases. Duke. Math. J. 54, 563-577 (1987)
4. Drinfeld, V., Degenerate affine Hecke algebras and Yangians. Funct. Anal. Appl. 20(1), 62-64 (1986)
5. Hill, D., Kujawa, J., Sussan, J.: Degenerate affine Hecke-Clifford algebras and type Q Lie superalgebras. (2009)
6. Jones, A., Nazarov, M.: Affine Sergeev algebra and q-analogues of the Young symmetrizers for projective representations of the symmetric group. Proc. London Math. Soc. 78, 481-512 (1999)
7. Kleshchev, A.: Completely splittable representations of symmetric groups. J. Algebra 181, 584-592 (1996)
8. Kleshchev, A.: Linear and Projective Representations of Symmetric Groups. Cambridge University Press, Cambridge (2005)
9. Kleshchev, A., Ram, A.: Homogeneous representations of Khovanov-Lauda algebras. (2008)
10. Leclerc, B.: Dual canonical bases, quantum shuffles and q-characters. Math. Z. 246(4), 691-732 (2004)
11. Lusztig, G.: Affine Hecke algebras and their graded version. J. Amer. Math. Soc. 2, 599-635 (1989)
12. Mathieu, O.: On the dimension of some modular irreducible representations of the symmetric group. Lett. Math. Phys. 38, 23-32 (1996)
13. Nazarov, M.: Young's orthogonal form of irreducible projective representations of the symmetric group. J. London Math. Soc. (2) 42(3), 437-451 (1990)
14. Nazarov, M.: Young's symmetrizers for projective representations of the symmetric group. Adv. Math. 127(2), 190-257 (1997)
15. Okounkov, A., Vershik, A.: A new approach to representation theory of symmetric groups. Selecta Math. (N.S.) 2, 581-605 (1996) J Algebr Comb (2010) 32: 15-58
16. Ram, A.: Skew shape representations are irreducible (English summary). In: Combinatorial and Geometric Representation Theory, Seoul,
2001. Contemp. Math., vol. 325, pp. 161-189. Amer. Math. Soc., Providence (2003)
17. Ruff, O.: Completely splittable representations of symmetric groups and affine Hecke algebras. J. Al- gebra 305, 1197-1211 (2006)
18. Wang, W.: Double affine Hecke-Clifford algebras for the spin symmetric group.
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