منابع مشابه
On the Spanning Vectors of Lusztig Cones
For each reduced expression i of the longest element w0 of the Weyl group W of a Dynkin diagram ∆ of type A, D or E, Lusztig defined a cone Ci such that there corresponds a monomial in the quantized enveloping algebra U of ∆ to each element of Ci and he asked under what circumstances these monomials belong to the canonical basis of U. In this paper, we consider the case where i is a reduced exp...
متن کاملThe Lusztig cones of a quantized enveloping algebra of type A
We show that for each reduced expression for the longest word in the Weyl group of type An, the corresponding cone arising in Lusztig’s description of the canonical basis in terms of tight monomials is simplicial, and construct explicit spanning vectors.
متن کاملRectangle diagrams for the Lusztig cones of quantized enveloping algebras of type A
Let U be the quantum group associated to a Lie algebra g of type An. The negative part U of U has a canonical basis B defined by Lusztig and Kashiwara, with favourable properties. We show how the spanning vectors of the cones defined by Lusztig [12], when regarded as monomials in Kashiwara’s root operators, can be described using a remarkable rectangle combinatorics. We use this to calculate th...
متن کامل0 Regions of linearity , Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A 4
Let Uq be the quantum group associated to a Lie algebra g of rank n. The negative part U− of U has a canonical basis B with favourable properties (see Kashiwara [6] and Lusztig [11, §14.4.6]). The approaches of Lusztig and Kashiwara lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in the Weyl group of g. We show that if g...
متن کاملKazhdan-lusztig Cells
These are notes for a talk on Kazhdan-Lusztig Cells for Hecke Algebras. In this talk, we construct the Kazhdan-Lusztig basis for the Hecke algebra associated to an arbitrary Coxeter group, in full multiparameter generality. We then use this basis to construct a partition of the Coxeter group into the Kazhdan-Lusztig cells and describe the corresponding cell representations. Finally, we speciali...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2004
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-04-00225-0