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Wee Liang Gan 《Advances in Mathematics》2006,205(2):599-630
We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of wreath product groups. 相似文献
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We give an elementary and direct combinatorial definition of opetopes in terms of trees, well-suited for graphical manipulation and explicit computation. To relate our definition to the classical definition, we recast the Baez-Dolan slice construction for operads in terms of polynomial monads: our opetopes appear naturally as types for polynomial monads obtained by iterating the Baez-Dolan construction, starting with the trivial monad. We show that our notion of opetope agrees with Leinster's. Next we observe a suspension operation for opetopes, and define a notion of stable opetopes. Stable opetopes form a least fixpoint for the Baez-Dolan construction. A final section is devoted to example computations, and indicates also how the calculus of opetopes is well-suited for machine implementation. 相似文献
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A complete group is one with a trivial center and with all automorphisms inner. This paper uses group cohomology to give a
sufficient condition for a finite semidirect product
G = N \rtimes H{G = N \rtimes H} with C
G
(N) ≤ N to be complete and proves a partial converse. These results are enough to fully characterize complete finite permutational
wreath products and to specialize that characterization in the case of finite standard wreath products. 相似文献
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Orthodox semidirect products and wreath products of monoids 总被引:17,自引:0,他引:17
Communicated by H.-J. Hoehnke 相似文献
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Hiroshi Mizukawa 《Journal of Algebraic Combinatorics》2007,25(2):189-215
The pair of groups, symmetric group S
2n
and hyperoctohedral group H
n
, form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions
of (S
2n
,H
n
) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials.
A wreath product generalization of the Gelfand pair (S
2n
,H
n
) is discussed in this paper. Then a multi-partition versions of the theory is constructed. The multi-partition version of
zonal polynomials are products of zonal polynomials and Schur functions and are obtained from a characteristic map from the
graded Hecke algebra into a multipartition version of the ring of symmetric functions.
Dedicated to Professor Eiichi Bannai on his 60th birthday. 相似文献
10.
Yugen Takegahara 《Advances in Mathematics》2007,209(2):526-546
Suppose that a group A contains only a finite number of subgroups of index d for each positive integer d. Let G?Sn be the wreath product of a finite group G with the symmetric group Sn on {1,…,n}. For each positive integer n, let Kn be a subgroup of G?Sn containing the commutator subgroup of G?Sn. If the sequence satisfies a certain compatible condition, then the exponential generating function of the sequence takes the form of a sum of exponential functions. 相似文献
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Generators and defining relations for wreath products of groups are given. Under a certain condition (conormality of generators),
they are minimal.
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 997–999, July, 2008. 相似文献
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Eric Marberg 《Israel Journal of Mathematics》2012,192(1):157-195
We prove that if a finite group H has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product H ? S n also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gel’fand model for wreath products of the form A ? S n with A abelian, and give an alternate proof of a recent result due to Adin, Postnikov and Roichman describing a particularly elegant Gel’fand model for the wreath product ? r ? S n . We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Postnikov and Roichman. 相似文献
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VALERIY G BARDAKOV OLEG V BRYUKHANOV KRISHNENDU GONGOPADHYAY 《Proceedings Mathematical Sciences》2017,127(1):99-108
We prove that the nilpotent product of a set of groups A 1,…,A s has finite palindromic width if and only if the palindromic widths of A i ,i=1,…,s,are finite. We give a new proof that the commutator width of F n ?K is infinite, where F n is a free group of rank n≥2 and K is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set. 相似文献
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Ievgen V. Bondarenko 《Archiv der Mathematik》2010,95(4):301-308
Let (G n , X n ) be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath product ${\ldots\wr G_2\wr G_1}Let (G
n
, X
n
) be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely
iterated permutational wreath product
?\wr G2\wr G1{\ldots\wr G_2\wr G_1} is topologically finitely generated if and only if the profinite abelian group ?n 3 1 Gn/G¢n{\prod_{n\geq 1} G_n/G'_n} is topologically finitely generated. As a corollary, for a finite transitive group G the minimal number of generators of the wreath power
G\wr ?\wr G\wr G{G\wr \ldots\wr G\wr G} (n times) is bounded if G is perfect, and grows linearly if G is non-perfect. As a by-product we construct a finitely generated branch group, which has maximal subgroups of infinite index. 相似文献
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