共查询到20条相似文献,搜索用时 93 毫秒
1.
Jeong-Ah Kim 《Mathematische Annalen》2005,332(1):17-35
We give a new realization of crystal graphs for irreducible highest weight modules over Uq(An(1)) in terms of the monomials introduced by H. Nakajima. We also discuss the natural connection between the monomial realization and other known realizations, path realization and Young wall realization.This research was supported by KOSEF Grant # 98-0701-01-5-L and BK21 Mathematical Sciences Division, Seoul National University. 相似文献
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《代数通讯》2013,41(8):2809-2825
Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In the previous articles, we constructed an n4-dimensional Hopf algebra Hn(p, q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω?1 , and studied the irreducible representations of Hn(1, q) and the finite dimensional representations of H3(1, q). In this article, we examine the finite-dimensional representations of Hn(l q), equivalently, of D(An(ω)) for any n ≥ 2. We investigate the indecomposable left Hn(1, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod Hn(1, q), and the Auslander-Reiten-quiver of Hn(1 q). 相似文献
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Consider the general linear group GLM over the complex field. The irreducible rational representations of the group GLM can be labeled by the pairs of partitions and such that the total number of non-zero parts of and does not exceed M. Let EQ4 be the irreducible representation corresponding to such a pair. Regard the direct product as a subgroup of GLN+M . Take any irreducible rational representation of GLN+M. The vector space comes with a natural action of the group GLN. Put n=. For any pair of standard Young tableaux of skew shapes respectively, we give a realization of as a subspace in the tensor product of n copies of defining representation of GLN, and of ñ copies of the contragredient representation ()*. This subspace is determined as the image of a certain linear operator on Wnñn. We introduce this operator by an explicit multiplicative formula. When M=0 and is an irreducible representation of GLN, we recover the known realization of as a certain subspace in the space of all traceless tensors in . Then the operator may be regarded as the rational analogue of the Young symmetrizer, corresponding to the tableau of shape . Even when M=0, our formula for is new. Our results are applications of the representation theory of the Yangian of the Lie algebra . In particular, is an intertwining operator between certain representations of the algebra on . We also introduce the notion of a rational representation of the Yangian . As a representation of , the image of is rational and irreducible.Mathematics Subject Classification (2000): 17B37, 20C30, 22E46, 81R50in final form: 10 July 2003 相似文献
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《代数通讯》2013,41(10):3467-3478
In the first part of this article, we describe the projective representations in the category of representations by modules of a quiver which does not contain any cycles and the quiver A ∞ as a subquiver, that is, the so-called rooted quivers. As a consequence of this, we show when the category of representations by modules of a quiver admits projective covers. In the second part, we develop a technique involving matrix computations for the quiver A ∞, which will allow us to characterize the projective representations of A ∞. This will improve some previous results and make more accurate the statement made in Benson (1991). We think this technique can be applied in many other general situations to provide information about the decomposition of a projective module. 相似文献
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Let A be a finite-dimensional algebra over a field k. The derived Picard group DPic
k
(A) is the group of triangle auto-equivalences of D>
b( mod A) induced by two-sided tilting complexes. We study the group DPic
k
(A) when A is hereditary and k is algebraically closed. We obtain general results on the structure of DPic
k
, as well as explicit calculations for many cases, including all finite and tame representation types. Our method is to construct a representation of DPic
k
(A) on a certain infinite quiver irr. This representation is faithful when the quiver of A is a tree, and then DPic
k
(A) is discrete. Otherwise a connected linear algebraic group can occur as a factor of DPic
k
(A). When A is hereditary, DPic
k
(A) coincides with the full group of k-linear triangle auto-equivalences of Db( mod A). Hence, we can calculate the group of such auto-equivalences for any triangulated category D equivalent to Db( mod A. These include the derived categories of piecewise hereditary algebras, and of certain noncommutative spaces introduced by Kontsevich and Rosenberg. 相似文献
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We study the K-theory of unital C*-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct
computational tools, but show that K-theory is far from being able to distinguish between various interesting examples. For example, when the algebra A is n-homogeneous, i.e., all irreducible representations are exactly of dimension n, then K*(A) is the topological K-theory of a related compact Hausdorff space, this generalises the classical Gelfand-Naimark theorem, but there are many inequivalent
homogeneous algebras with the same related topological space. For general A we give a spectral sequence computing K*(A) from a sequence of topological K-theories of related spaces. For A generated by two idempotents, this becomes a 6-term long exact sequence. 相似文献
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Jason Bandlow Anne Schilling Nicolas M. Thiéry 《Journal of Algebraic Combinatorics》2010,31(2):217-251
The affine Dynkin diagram of type A
n
(1) has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator.
In this paper we show that the only irreducible type A
n
crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that
on the tensor product of two type A
n
crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary
number of tensor factors. Our results are in agreement with Kashiwara’s conjecture that all ‘good’ affine crystals are tensor
products of Kirillov-Reshetikhin crystals. 相似文献
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Dong-Uy Shin 《代数通讯》2013,41(1):129-142
In this article, we give a new realization of crystal bases for irreducible highest weight modules over U q (G 2) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization. Communicated by K. Misra 相似文献
14.
John W. Snow 《Algebra Universalis》2000,44(1-2):169-185
Suppose is a set of operations on a finite set A. Define PPC() to be the smallest primitive positive clone on A containing . For any finite algebra A, let PPC#(A) be the smallest number n for which PPC(CloA) = PPC(Clo
n
A). S. Burris and R. Willard [2] conjectured that PPC#(A) ≤|A| when CloA is a primitive positive clone and |A| > 2. In this paper, we look at how large PPC#(A) can be when special conditions are placed on the finite algebra A. We show that PPC#(A) ≤|A| holds when the variety generated by A is congruence distributive, Abelian, or decidable. We also show that PPC#(A) ≤|A| + 2 if A generates a congruence permutable variety and every subalgebra of A is the product of a congruence neutral algebra and an Abelian algebra. Furthermore, we give an example in which PPC#(A) ≥|A| - 1)2 so that these results are not vacuous.
Received August 30, 1999; accepted in final form April 4, 2000. 相似文献
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Cristian Lenart 《Discrete Mathematics》2011,(4):887
A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. The inversion statistic, which is the more intricate one, suffices for specializing a closely related formula to one for the type A Hall–Littlewood Q-polynomials (spherical functions on p-adic groups). An apparently unrelated development, at the level of arbitrary finite root systems, led to Schwer’s formula (rephrased and rederived by Ram) for the Hall–Littlewood P-polynomials of arbitrary type. The latter formula is in terms of so-called alcove walks, which originate in the work of Gaussent–Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by deriving a Haglund–Haiman–Loehr type formula for the Hall–Littlewood P-polynomials of type A from Ram’s version of Schwer’s formula via a “compression” procedure. 相似文献
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Chun Lan JIANG Yong Fei JIN Zong Yao WANG 《数学学报(英文版)》2007,23(8):1385-1390
Abstract Let H be a complex seperable Hilbert space and ~(Jt~) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative. 相似文献
19.
Let A be a tame concealed or tubular algebra and d the dimension-vector of a periodic module with respect to the action of the Auslander–Reiten translation. We prove that the affine variety mod
A
(d) of all A-modules of dimension-vector d is a normal complete intersection. Moreover, we show that a module M in mod
A
(d) is nonsingular if and only if Ext
A
2(M,M)=0. 相似文献
20.
Jae-Hoon Kwon 《Journal of Combinatorial Theory, Series A》2011,118(7):2131-2156
We give a new combinatorial realization of the crystal base of the modified quantized enveloping algebras of type A+∞ or A∞. It is obtained by describing the decomposition of the tensor product of a highest weight crystal and a lowest weight crystal into extremal weight crystals, and taking its limit using a tableaux model of extremal weight crystals. This realization induces in a purely combinatorial way a bicrystal structure of the crystal base of the modified quantized enveloping algebras and hence its Peter-Weyl type decomposition generalizing the classical RSK correspondence. 相似文献