A generalization of adjoint crystals for the quantized affine algebras of type A n (1) , C n (1) and D n+1 (2)
Ryosuke Kodera
DOI: 10.1007/s10801-009-0174-3
Abstract
We generalize Benkart-Frenkel-Kang-Lee's adjoint crystals and describe their crystal structure for type A n (1), C n (1) and D n+1 (2).
Pages: 491–514
Keywords: keywords crystal base; quantized affine algebra; kirillov-reshetikhin module
Full Text: PDF
References
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0. Int. Math. Res. Not., 10312 (2006)
2. Chari, V.: On the fermionic formula and the Kirillov-Reshetikhin conjecture. Int. Math. Res. Not. 12, 629-654 (2001)
3. Hernandez, D.: Kirillov-Reshetikhin conjecture: the general case.
4. Hong, J., Kang, S.-J.: Introduction to Quantum Groups and Crystal Bases. Graduate Studies in Mathematics, vol.
42. American Mathematical Society, Providence (2002)
5. Humphreys, J.E.: Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, vol.
9. Springer, New York (1978); second printing, revised
6. Kac, V.G.: Infinite-Dimensional Lie Algebras, 3rd edn. Cambridge University Press, Cambridge (1990) J Algebr Comb (2009) 30: 491-514
7. Kang, S.-J., Kashiwara, M., Misra, K.C.: Crystal bases of Verma modules for quantum affine Lie algebras. Compos. Math. 92(3), 299-325 (1994)
8. Kang, S.-J., Kashiwara, M., Misra, K.C., Miwa, T., Nakashima, T., Nakayashiki, A.: Perfect crystals of quantum affine Lie algebras. Duke Math. J. 68(3), 499-607 (1992)
9. Kashiwara, M.: On crystal bases of the Q-analogue of universal enveloping algebras. Duke Math. J. 63(2), 465-516 (1991) (3)
10. Kashiwara, M., Misra, K.C., Okado, M., Yamada, D.: Perfect crystals for Uq (D ). J. Algebra 4 317(1), 392-423 (2007)
11. Kashiwara, M., Nakashima, T.: Crystal graphs for representations of the q-analogue of classical Lie algebras. J. Algebra 165(2), 295-345 (1994)
12. Okado, M.: X = M conjecture, Combinatorial aspect of integrable systems. MSJ Mem., Math. Soc. Jpn., Tokyo 17, 43-73 (2007)
13. Okado, M., Schilling, A.: Existence of Kirillov-Reshetikhin crystals for nonexceptional types. Represent. Theory 12, 186-207 (2008) (1)
14. Schilling, A., Sternberg, P.: Finite-dimensional crystals B2,s for quantum affine algebras of type Dn .