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对于Kazhdan-Lusztig多项式Py,w(q),μ(y,w)为它的首项系数(简称KL系数).首项系数在李代数及其表示理论中起着重要的作用.在文章中,W为A3型仿射Weyl群,通过它对应的Hecke代数的性质及其KL基{Cw}的乘积计算,以及不可约模在张量积中的重数公式,给出了A3型仿射Weyl群最低双边胞腔上的KL系数. 相似文献
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本文研究了胞腔代数的直接构造问题.利用构造箭图并在其上添加关系的方法,获得了一种不可分解胞腔代数的构造方法.证明了总存在不可分解的胞腔代数A(对λ∈S(n))使得其卡当矩阵具有形如{n,1,…,1}的谱,从而拓广了胞腔代数的构造途径. 相似文献
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一个带有非平凡幂等元的结合代数带有自然的Rota-Baxter代数结构.本文研究胞腔代数的不同拟幂等元给出的Rota-Baxter结构间的同构关系. 相似文献
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周新建 《数学的实践与认识》2016,(8):257-262
描述了(B)n型仿射Weyl群a值为5的A2×A11×A12型左胞腔的个数.并计算出当n=7时,这样的左胞腔个数为20个;当n≥8时,左胞腔个数为1/6(2n3-21n2+ 417n-510)个. 相似文献
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《数学的实践与认识》2016,(8)
描述了_n型仿射Weyl群a值为5的A_2×A_(11)×A_(12)型左胞腔的个数.并计算出当n=7时,这样的左胞腔个数为20个;当n≥8时,左胞腔个数为1/6(2n~3-21n~2+417n-510)个. 相似文献
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描述了_n型仿射Weyl群a值为5的A_2×A_(12)2型左胞腔的个数.并计算出当n=8时,这样的左胞腔个数为8个;当n=9时,这样的左胞腔个数为35个;当n≥10时,左胞腔个数为1/(30)(n2型左胞腔的个数.并计算出当n=8时,这样的左胞腔个数为8个;当n=9时,这样的左胞腔个数为35个;当n≥10时,左胞腔个数为1/(30)(n5-20n5-20n4-155n4-155n3+7520n3+7520n2-7254n+220240)个. 相似文献
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本文研究了无限维李代数so2l(Q).利用其明确的生成元,确定了所有的非交换Poisson代数结构,推广了有限维的情形. 相似文献
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Graham and Lehrer have defined cellular algebras and developed a theory that allows in particular to classify simple representations of finite dimensional cellular algebras. Many classes of finite dimensional algebras, including various Hecke algebras and diagram algebras, have been shown to be cellular, and the theory due to Graham and Lehrer successfully has been applied to these algebras.We will extend the framework of cellular algebras to algebras that need not be finite dimensional over a field. Affine Hecke algebras of type A and infinite dimensional diagram algebras like the affine Temperley–Lieb algebras are shown to be examples of our definition. The isomorphism classes of simple representations of affine cellular algebras are shown to be parameterised by the complement of finitely many subvarieties in a finite disjoint union of affine varieties. In this way, representation theory of non-commutative algebras is linked with commutative algebra. Moreover, conditions on the cell chain are identified that force the algebra to have finite global cohomological dimension and its derived category to admit a stratification; these conditions are shown to be satisfied for the affine Hecke algebra of type A if the quantum parameter is not a root of the Poincaré polynomial. 相似文献
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席南华 《数学物理学报(B辑英文版)》2009,29(3):515-526
Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper. 相似文献
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Bogdan Ion 《Compositio Mathematica》2003,139(1):67-84
We prove the existence of an involution on double affine Hecke algebras. This involution plays a central role in the theory of Macdonald polynomials, being responsible for a Fourier type duality and allowing the construction of affine intertwiners. 相似文献
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Dung Nguyen Tien 《Algebras and Representation Theory》2014,17(5):1359-1400
Let R be a commutative noetherian domain. The q-Brauer algebras over R are shown to be cellular algebras in the sense of Graham and Lehrer. In particular, they are iterated inflations of Hecke algebras of type A. When R is a field of arbitrary characteristic, we determine for which parameters the q-Brauer algebras are quasi-hereditary. Then, using the general theory of cellular algebras we parametrize all irreducible representations of q-Brauer algebras. 相似文献
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A. P. Isaev 《Theoretical and Mathematical Physics》2007,150(2):187-202
We consider integrable open chain models formulated in terms of the generators of affine Hecke algebras. We use the fusion
procedure to construct the hierarchy of commutative elements, which are analogues of the commutative transfer matrices. These
elements satisfy a set of functional relations generalizing functional relations for a family of transfer matrices in solvable
spin chain models of the Uq(gl(n|m)) type.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 219–236, February, 2007. 相似文献
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G. Pouchin 《Journal of Algebra》2009,321(1):230-247
After establishing a geometric Schur–Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts have nice ideals coming from geometry, allowing duality for quotients. Some of the quotients of the positive affine Hecke algebra are then identified to some cyclotomic Hecke algebras and the geometric setting allows the construction of canonical bases. 相似文献
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M. V. Zaitsev 《Mathematical Notes》1997,62(1):80-86
In this paper the identities of the complex affine Kac-Moody algebras are studied. It is proved that the identities of twisted
affine algebras coincide with those of the corresponding nontwisted algebras. Moreover, in the class of nontwisted affine
Kac-Moody algebras, each of these algebras is uniquely defined by its identities. It is shown that the varieties of affine
algebras, as well as the varieties defined by finitely generated three-step solvable Lie algebras, have exponential growth.
Translated fromMatematicheskie Zametki, Vol. 62 No. 1, pp. 95–102, July 1997.
Translated by A. I. Shtern 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
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《Indagationes Mathematicae》2017,28(4):736-748
Ram and Rammage have introduced an automorphism and Clifford theory on affine Hecke algebras. Here we will extend them to cyclotomic Hecke algebras and rational Cherednik algebras. 相似文献