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Relative Kazhdan–lusztig Cells
 REPRESENTATION THEORY AN ELECTRONIC JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
, 2006
"... In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative ” setting, with respect to a parabolic subgroup WI ⊆ W. This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multiparameter) Iwahori–Hecke algebra with respect to WI. We obtain tw ..."
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Cited by 32 (6 self)
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In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative ” setting, with respect to a parabolic subgroup WI ⊆ W. This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multiparameter) Iwahori–Hecke algebra with respect to WI. We obtain
Abstract KazhdanLusztig theories
 TÔHOKU MATH. J
, 1993
"... In this paper, we prove two main results. The first establishes that Lusztig's conjecture for the characters of the irreducible representations of a semisimple algebraic group in positive characteristic is equivalent to a simple assertion that certain pairs of irreducible modules have nonspli ..."
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Cited by 48 (27 self)
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In this paper, we prove two main results. The first establishes that Lusztig's conjecture for the characters of the irreducible representations of a semisimple algebraic group in positive characteristic is equivalent to a simple assertion that certain pairs of irreducible modules have non
Permutations with KazhdanLusztig polynomial . . .
, 2009
"... Using resolutions of singularities introduced by Cortez and a method for calculating KazhdanLusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with KazhdanLusztig polynomial Pid,w(q) = 1 + q h for some h. ..."
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Cited by 1 (0 self)
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Using resolutions of singularities introduced by Cortez and a method for calculating KazhdanLusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with KazhdanLusztig polynomial Pid,w(q) = 1 + q h for some h.
KAZHDAN–LUSZTIG POLYNOMIALS FOR CERTAIN VARIETIES OF INCOMPLETE FLAGS
"... We give explicit formulas for the KazhdanLusztig P and Rpolynomials for permutations coming from the variety F1,n−1 of incomplete flags consisting of a line and a hyperplane. ..."
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Cited by 7 (0 self)
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We give explicit formulas for the KazhdanLusztig P and Rpolynomials for permutations coming from the variety F1,n−1 of incomplete flags consisting of a line and a hyperplane.
Quasisymmetric functions and KazhdanLusztig polynomials
, 2007
"... We associate a quasisymmetric function to any Bruhat interval in a general Coxeter group. This association can be seen to be a morphism of Hopf algebras to the subalgebra of all peak functions, leading to an extension of the cdindex of convex polytopes. We show how the KazhdanLusztig polynomial ..."
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Cited by 22 (1 self)
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of the Bruhat interval can be expressed in terms of this complete cdindex and otherwise explicit combinatorially defined polynomials. In particular, we obtain the simplest closed formula for the KazhdanLusztig polynomials that holds in complete generality.
KazhdanLusztig Polynomials And Canonical Basis
 Transform. Groups
, 1997
"... In this paper we show that the KazhdanLusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uq sl k . We also use known results about ..."
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Cited by 23 (3 self)
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In this paper we show that the KazhdanLusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor power of the fundamental representation of the quantum group Uq sl k . We also use known results about
Lattice paths and KazhdanLusztig polynomials
 J. Amer. Math. Soc
, 1998
"... In their fundamental paper [18] Kazhdan and Lusztig defined, for every Coxeter group W, a family of polynomials, indexed by pairs of elements of W, which have become known as the KazhdanLusztig polynomials of W (see, e.g., [17], Chap. 7). These polynomials are intimately related to the Bruhat order ..."
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Cited by 20 (4 self)
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In their fundamental paper [18] Kazhdan and Lusztig defined, for every Coxeter group W, a family of polynomials, indexed by pairs of elements of W, which have become known as the KazhdanLusztig polynomials of W (see, e.g., [17], Chap. 7). These polynomials are intimately related to the Bruhat
KAZHDAN–LUSZTIG CELLS AND THE MURPHY BASIS
, 2005
"... Let H be the Iwahori–Hecke algebra associated with Sn, the symmetric group on n symbols. This algebra has two important bases: the Kazhdan–Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction of the repr ..."
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Cited by 17 (6 self)
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Let H be the Iwahori–Hecke algebra associated with Sn, the symmetric group on n symbols. This algebra has two important bases: the Kazhdan–Lusztig basis and the Murphy basis. While the former admits a deep geometric interpretation, the latter leads to a purely combinatorial construction
Results 1  10
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807,032