MetaCart Sign in to MyCiteSeerX

Include Citations | Advanced Search | Help

Disambiguated Search | Include Citations | Advanced Search | Help

On Crystal Bases (1995) [9 citations — 0 self]

by Masaki Kashiwara
Add To MetaCart

Abstract:

The crystal base is introduced by the investigation of the quantized universal enveloping algebra at q = 0. It carries a combinatorial structure, which permits us a combinatorial study of representations. We explain here this notion and its properties. Contents 0 .

Citations

99 Introduction to quantum groups – Lusztig - 1993
36 Crystal graphs for representations of the q-analogue of classical Lie algebras – KASHIWARA, NAKASHIMA - 1994
31 Crystallizing the q-analogue of universal enveloping algebras – Kashiwara - 1990
31 Algebraic analysis of solvable lattice models – Jimbo, Miwa - 1995
31 A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras – Littelmann - 1994
8 String bases for quantum groups of type Ar – Berenstein, Zelevinsky - 1993
4 Base and a Generalization of the LittlewoodRichardson Rule for the Classical Lie Algebras – Nakashima - 1993
4 A comparison of bases of quantized enveloping algebras – Grojnowski, Lusztig - 1993
3 crystal bases of quantum groups – Global - 1993
3 crystals of quantum ane Lie algebra – Perfect - 1992
3 PBW basis of quantized universal enveloping algebras – Saito - 1994
2 base and Littelmann's re Demazure character formula – Crystal - 1993
1 bases of modi quantized enveloping algebra, Duke Math – Crystal - 1994
1 base for the basic representation of Uq ( b sl 2 – Misra, Miwa - 1990
1 Vertex models and crystals – Kang, Kashiwara, et al. - 1992
1 Crystal bases of Verma modules for quantum ane Lie algebras, Compositio Mathematica 92 – Kang, Kashiwara, et al. - 1994
1 T.Nakashima and T.Tokihiro, Quantum ane symmetry in Vertex models – Idzumi, Jimbo - 1993
1 root operators in representation theory, Ann. Math. (to appear). As for the canonical base of G.Lusztig, see the following book and the references inside – Path
1 for quantum Demazure modules,II, in Algebraic groups and their generalization: quantum and in methods – Lakshmibai - 1994
1 algebra and the Yang-Baxter equation, Soviet Math.Dokl.(English translation – Drinfeld - 1985
1 A q-dierence analogue of U(g) and the Yang-Baxter equation, Lett.Math.Phys – Jimbo - 1985
1 On quantum groups, J.Algebra 131 – Lusztig - 1990