Crystal bases of Verma modules for quantum affine Lie algebras

Seok-Jin Kang; Masaki Kashiwara; Kailash C. Misra

Compositio Mathematica (1994)

  • Volume: 92, Issue: 3, page 299-325
  • ISSN: 0010-437X

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Kang, Seok-Jin, Kashiwara, Masaki, and Misra, Kailash C.. "Crystal bases of Verma modules for quantum affine Lie algebras." Compositio Mathematica 92.3 (1994): 299-325. <http://eudml.org/doc/90309>.

@article{Kang1994,
author = {Kang, Seok-Jin, Kashiwara, Masaki, Misra, Kailash C.},
journal = {Compositio Mathematica},
keywords = {energy function; path realization; crystal base; Verma modules; quantum affine Lie algebras},
language = {eng},
number = {3},
pages = {299-325},
publisher = {Kluwer Academic Publishers},
title = {Crystal bases of Verma modules for quantum affine Lie algebras},
url = {http://eudml.org/doc/90309},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Kang, Seok-Jin
AU - Kashiwara, Masaki
AU - Misra, Kailash C.
TI - Crystal bases of Verma modules for quantum affine Lie algebras
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 92
IS - 3
SP - 299
EP - 325
LA - eng
KW - energy function; path realization; crystal base; Verma modules; quantum affine Lie algebras
UR - http://eudml.org/doc/90309
ER -

References

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  1. [D] Drinfeld, V.G.: Hopf algebra and the Yang-Baxter equation. Soviet Math. Dokl.32 (1985) 254-258. Zbl0588.17015
  2. [J] Jimbo, M.: A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys.10 (1985) 63-69. Zbl0587.17004MR797001
  3. [JMMO] Jimbo, M., Misra, K.C., Miwa, T. and Okado, M.: Combinatorics of representations of U q(šl(n)) at q = 0. Commun. Math. Phys.136 (1991) 543-566. Zbl0749.17015MR1099695
  4. [K1] Kashiwara, M.: Crystalizing the q-analogue of universal enveloping algebras. Commun. Math. Phys.133 (1990) 249-260. Zbl0724.17009MR1090425
  5. [K2] Kashiwara, M.: On crystal bases of the q-analogue of universal enveloping algebras. Duke Math. J.63 (1991) 465-516. Zbl0739.17005MR1115118
  6. [KKM] Kang, S.-J., Kashiwara, M. and Misra, K.C.: Crystal bases of Verma modules for quantum affine Lie algebras. RIMS preprint887 (1992). 
  7. [KMN1] Kang, S.-J., Kashiwara, M., Misra, K.C., Miwa, T., Nakashima, T. and Nakayashiki, A.: Vertex models and crystals. C. R. Acad. Sci. Paris t.315, Série I (1992) 375-380. Zbl0776.17008MR1179041
  8. [KMN2] Kang, S.-J., Kashiwara, M., Misra, K.C., Miwa, T., Nakashima, T. and Nakayashiki, A.: Affine crystals and vertex models. Int. J. Mod. Phys. A. Suppl. 1A (1992), 449-484. Zbl0925.17005MR1187560
  9. [KMN3] Kang, S.-J., Kashiwara, M., Misra, K.C., Miwa, T., Nakashima, T. and Nakayashiki, A.: Perfect crystals of quantum affine Lie algebras. Duke Math. J.68 (1992) 499-607. Zbl0774.17017MR1194953
  10. [KM1] Kang, S.-J. and Misra, K.C.: Crystal bases and tensor product decomposition of Uq(G2)-modules. J. Algebras, to appear. Zbl0808.17006MR1265857
  11. [KM2] Kang, S.-J. and Misra, K.C.: The quantum affine Lie algebra Uq(C(1)n) and crystal base. Manuscript in preparation. 
  12. [KN] Kashiwara, M. and Nakashima, T.: Crystal graphs for representations of the q-analogue of classical Lie algebras. RIMS preprint 767 (1991), J. Algebra, to appear. Zbl0808.17005MR1273277
  13. [Li] Littelmann, P.: Crystal graphs and Young tableaux. Preprint (1991). Zbl0831.17004MR1338967
  14. [Lu1] Lusztig, G.I.: Canonical bases arising from quantized enveloping algebra. J. Amer. Math. Soc.3 (1990) 447-498. Zbl0703.17008MR1035415
  15. [Lu2] Lusztig, G.I.: Canonical bases arising from quantized enveloping algebra II. Progr. Theor. Phys. Suppl.102 (1990) 175-201. Zbl0776.17012MR1182165
  16. [LG] Lusztig, G.I. and Grojnowski, I.: A comparison of bases of quantized enveloping algebras. Linear algebraic groups and their representations. Contemporary Mathematics153 (1993) 11-19. Zbl1009.17502MR1247495
  17. [MM] Misra, K.C. and Miwa, T.: Crystal base for the basic representation of Uq(šl(n)). Commun. Math. Phys.134 (1990) 79-88. Zbl0724.17010MR1079801
  18. [N] Nakashima, T.: Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras. Commun. Math. Phys.154 (1993) 215-243. Zbl0795.17016MR1224078

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