共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the Schur elements associated to the simple modules of the Ariki–Koike algebra. We first give a cancellation-free
formula for them so that their factors can be easily read and programmed. We then study direct applications of this result.
We also complete the determination of the canonical basic sets for cyclotomic Hecke algebras of type G(l,p,n) in characteristic 0. 相似文献
2.
3.
We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda
algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification
theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive characteristic. 相似文献
4.
We construct irreducible representations of affine Khovanov–Lauda–Rouquier algebras of arbitrary finite type. The irreducible
representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that of Bernstein
and Zelevinsky for affine Hecke algebras of type A. The highest weights of irreducible modules are given by the so-called good words, and the highest weights of the ‘cuspidal
modules’ are given by the good Lyndon words. In a sense, this has been predicted by Leclerc. 相似文献
5.
Jun Ding 《Journal of Pure and Applied Algebra》2006,205(2):296-309
In this paper, we first introduce a notion of semisimple system with parameters, then we establish Lusztig's isomorphism theorem for any cellular semisimple system with parameters. As an application, we obtain Lusztig's isomorphism theorem for Ariki-Koike algebras, cyclotomic q-Schur algebras and Birman-Murakami-Wenzl algebras. Second, using the results for certain Ariki-Koike algebras, we prove an analogue of Lusztig's isomorphism theorem for the cyclotomic Hecke algebras of type G(p,p,n) (which are not known to be cellular in general). These generalize earlier results of [G. Lusztig, On a theorem of Benson and Curtis, J. Algebra 71 (1981) 490-498.] on such isomorphisms for Iwahori-Hecke algebras associated to finite Weyl groups. 相似文献
6.
Deke Zhao 《Monatshefte für Mathematik》2014,173(3):441-453
In this paper we give the symbolical formula and cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some applications, we show that the Schur elements are symmetric polynomials with rational integer coefficients and give a different proof of Ariki–Mathas–Rui’s criterion on the semisimplicity of the degenerate cyclotomic Hecke algebras. 相似文献
7.
We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac–Moody algebras and their integrable highest weight modules. 相似文献
8.
John Enyang 《Journal of Algebraic Combinatorics》2007,26(3):291-341
A construction of bases for cell modules of the Birman–Murakami–Wenzl (or B–M–W) algebra B
n
(q,r) by lifting bases for cell modules of B
n−1(q,r) is given. By iterating this procedure, we produce cellular bases for B–M–W algebras on which a large Abelian subalgebra,
generated by elements which generalise the Jucys–Murphy elements from the representation theory of the Iwahori–Hecke algebra
of the symmetric group, acts triangularly. The triangular action of this Abelian subalgebra is used to provide explicit criteria,
in terms of the defining parameters q and r, for B–M–W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration
here, of certain results from the Specht module theory of the Iwahori–Hecke algebra of the symmetric group.
Research supported by Japan Society for Promotion of Science. 相似文献
9.
10.
We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras
which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras
defined over fields of characteristic zero are now known in principle.
Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002 相似文献
11.
Clinton Boys 《Algebras and Representation Theory》2016,19(1):235-253
We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman’s hash involution. We compute the rank of these algebras and construct a full set of irreducible representations in the semisimple case, generalising Mitsuhashi’s results Mitsuhashi (J. Alg. 240 535–558 2001, J. Alg. 264 231–250 2003). 相似文献
12.
Jonathan Brundan 《Advances in Mathematics》2009,222(6):1883-251
In recent joint work with Wang, we have constructed graded Specht modules for cyclotomic Hecke algebras. In this article, we prove a graded version of the Lascoux-Leclerc-Thibon conjecture, describing the decomposition numbers of graded Specht modules over a field of characteristic zero. 相似文献
13.
《Journal of Pure and Applied Algebra》2023,227(3):107229
We introduce the notion of ?Schur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ?Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ?Scuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ?Schur superalgebras. 相似文献
14.
15.
Kei Yuen Chan 《Algebras and Representation Theory》2018,21(4):859-895
In this paper, we establish connections between the first extensions of simple modules and certain filtrations of of standard modules in the setting of graded Hecke algebras. The filtrations involved are radical filtrations and Jantzen filtrations. Our approach involves the use of information from the Langlands classification as well as some deeper understanding on some structure of some modules. Such module arises from the image of a Knapp-Stein type intertwining operator and is a quotient of a generalized standard module. As an application, we compute the Ext-groups for irreducible modules in a block for the graded Hecke algebra of type C 3, assuming the truth of a version of Jantzen conjecture. 相似文献
16.
Claus Michael Ringel 《Archiv der Mathematik》2008,91(3):218-225
We are going to determine the self-injective cluster-tilted algebras. All are of finite representation type and special biserial.
There are two different classes. The first class are the self-injective serial (or Nakayama) algebras with n ≥ 3 simple modules and Loewy length n–1. The second class of algebras has an even number 2m of simple modules; m indecomposable projective modules have length 3, the remaining m have length m + 1.
Received: 28 May 2007 相似文献
17.
José A. de la Peña 《Algebras and Representation Theory》2014,17(3):905-930
Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation ? A as the automorphism of the Grothendieck group K 0(A) induced by the Auslander-Reiten translation τ in the derived category Der(modA) of the module category modA of finite dimensional left A-modules. We say that A is an algebra of cyclotomic type if the characteristic polynomial χ A of ? A is a product of cyclotomic polynomials. There are many examples of algebras of cyclotomic type in the representaton theory literature: hereditary algebras of Dynkin and extended Dynkin types, canonical algebras, some supercanonical and extended canonical algebras. Among other results, we show that: (a) algebras satisfying the fractional Calabi-Yau property have periodic Coxeter transformation and are, therefore, of cyclotomic type, and (b) algebras whose homological form h A is non-negative are of cyclotomic type. For an algebra A of cyclotomic type we describe the shape of the Auslander-Reiten components of Der(modA). 相似文献
18.
We extend Schur–Weyl duality to an arbitrary level l ≥ 1, level one recovering the classical duality between the symmetric and general linear groups. In general, the symmetric
group is replaced by the degenerate cyclotomic Hecke algebra over parametrized by a dominant weight of level l for the root system of type A∞. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed
by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic category for the general linear Lie algebra.
相似文献
19.
Vanessa Miemietz 《Algebras and Representation Theory》2008,11(4):369-405
Ariki’s and Grojnowski’s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain – under certain restrictions on the eigenvalues of the lattice operators – analogous multiplicity-one
results and a classification of irreducibles with partial branching rules as in type A.
Research supported by the Studienstiftung des deutschen Volkes. 相似文献
20.
The reducibility of the Specht modules for the Iwahori–Hecke algebras in type A is still open in the case where the defining parameter q equals ?1. We prove the reducibility of a large class of Specht modules for these algebras. 相似文献