共查询到19条相似文献,搜索用时 46 毫秒
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In order to study the representation theory of Lie algebras and algebraic groups, Cline, Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasihereditary algebras. Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,..., n} such that HomB(P(i), P(j)) = 0 for i 〉 j. In this paper, it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l, then its dual extension algebra A = .A(B) has also the Kazhdan-Lusztig theory relative to the length function l. 相似文献
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表达一个判断的语句称为命题,命题是由题设和题断构成。证明一个命题成立,有直接证法和间接证法。反证法属于间接证法。一般来说,大多数命题的证明是由直接证法给出的,但是当直接证法不易证明甚至无法证明时,运用反证法,有时可以收到证明既简练又确切的良好效果。因此反证法是一种重要的证明方法。然而多年来,一些人有片面的认识,认为反 相似文献
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本文在三角多项式类中讨论了2π周期函数的一类Birkhoff型等距结点的三角插值问题,给出了此问题有解的充要条件,并构造出插值基. 相似文献
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Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation, we investigate the polynomial function model in Born-Infeld theory in this paper with the form of-([1-a(φ)2]φ) = λf(φ(x)),where λ > 0 is a real parameter, f ∈ C2(0, +∞) is a nonlinear function. We are interested in the exact number of positive solutions of the above nonlinear equation. We specifically develop for the problem combined with a... 相似文献
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Federico Incitti 《Journal of Combinatorial Theory, Series A》2006,113(7):1332-1350
In this paper, we solve the conjecture about the combinatorial invariance of Kazhdan-Lusztig polynomials for the first open cases, showing that it is true for intervals of length 5 and 6 in the symmetric group. We also obtain explicit formulas for the R-polynomials and for the Kazhdan-Lusztig polynomials associated with any interval of length 5 in any Coxeter group, showing in particular what they look like in the symmetric group. 相似文献
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We consider the Kazhdan-Lusztig polynomials P
u,v
(q) indexed by permutations u, v having particular forms with regard to their monotonicity patterns. The main results are the following. First we obtain a simplified recurrence relation satisfied by P
u,v
(q) when the maximum value of v Sn occurs in position n – 2 or n – 1. As a corollary we obtain the explicit expression for Pe,3 4 ... n 1 2(q) (where e denotes the identity permutation), as a q-analogue of the Fibonacci number. This establishes a conjecture due to M. Haiman. Second, we obtain an explicit expression for Pe, 3 4 ... (n – 2) n (n – 1) 1 2(q). Our proofs rely on the recurrence relation satisfied by the Kazhdan-Lusztig polynomials when the indexing permutations are of the form under consideration, and on the fact that these classes of permutations lend themselves to the use of induction. We present several conjectures regarding the expression for P
u,v
(q) under hypotheses similar to those of the main results. 相似文献
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Ewan Delanoy 《Journal of Algebraic Combinatorics》2006,24(4):437-463
We show that for Bruhat intervals starting from the identity in Coxeter groups the conjecture of Lusztig and Dyer holds, that is, the R-polynomials and the Kazhdan-Lusztig polynomials defined on [e,u] only depend on the isomorphism type of [e,u]. To achieve this we use the purely poset-theoretic notion of special matching. Our approach is essentially a synthesis of the explicit formula for special matchings discovered by Brenti and the general special matching machinery developed by Du Cloux. 相似文献
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Francesco Brenti 《Journal of the American Mathematical Society》1998,11(2):229-259
The purpose of this paper is to present a new non-recursive combinatorial formula for the Kazhdan-Lusztig polynomials of a Coxeter group . More precisely, we show that each directed path in the Bruhat graph of has a naturally associated set of lattice paths with the property that the Kazhdan-Lusztig polynomial of is the sum, over all the lattice paths associated to all the paths going from to , of where , and are three natural statistics on the lattice path.
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Fabrizio Caselli 《Journal of Algebraic Combinatorics》2003,18(3):171-187
We find an explicit formula for the Kazhdan-Lusztig polynomials P
ui,a,v
i of the symmetric group
(n) where, for a, i, n
such that 1 a i n, we denote by u
i,a = s
a
s
a+1 ··· s
i–1 and by v
i the element of
(n) obtained by inserting n in position i in any permutation of
(n – 1) allowed to rise only in the first and in the last place. Our result implies, in particular, the validity of two conjectures of Brenti and Simion [4, Conjectures 4.2 and 4.3], and includes as a special case a result of Shapiro, Shapiro and Vainshtein [13, Theorem 1]. All the proofs are purely combinatorial and make no use of the geometry of the corresponding Schubert varieties. 相似文献
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HeChun Zhang 《中国科学A辑(英文版)》2009,52(3):401-416
Canonical bases of the tensor powers of the natural -module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is
generalized in several directions. We first construct the canonical bases of the ℤ2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra O
q
(M
m|n
) of a quantum (m,n) × (m,n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for by applying a quantum analogue of the Borel-Weil construction.
This work was supported by National Natural Science Foundation of China (Grant No. 10471070) 相似文献
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Yunchuan Yin 《代数通讯》2013,41(2):547-565
ABSTRACT The “W-graph” concept was introduced by Kazhdan and Lusztig in their influential article Kazhdan and Lusztig (1979). If W is a Coxeter group, then a W-graph provides a method for constructing a matrix representation of the Hecke algebra ? associated with W (the degree of the representation being the number of vertices of the W-graph). The aim of this note is to explicitly construct all the irreducible representations of ? when W is of type D 4 and D 5. 相似文献
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This paper is a sequel to [4]. We establish the minimal basis theory for the centralizers of parabolic subalgebras of Iwahori-Hecke algebras associated to finite Coxeter groups of any type, generalizing the approach introduced in [3] from centres to the centralizer case. As a pro-requisite, we prove a reducibility property in the twisted J-conjugacy classes in finite Coxeter groups, which is a generalization of results in [7] and [4].2000 Mathematics Subject Classification: 20C08, 20F55 相似文献
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The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A
construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving
explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed
by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist
algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well
as complex reflection groups.
Received: July 25, 2001 相似文献