共查询到20条相似文献,搜索用时 15 毫秒
1.
We develop a number of statistical aspects of symmetric groups (mostly dealing with the distribution of cycles in various subsets of Sn), asymptotic properties of (ordinary) characters of symmetric groups, and estimates for the multiplicities of root number functions of these groups. As main applications, we present an estimate for the subgroup growth of an arbitrary Fuchsian group, a finiteness result for the number of Fuchsian presentations of such a group (resolving a long-standing problem of Roger Lyndon), as well as a proof of a well-known conjecture of Roichman concerning the mixing time of random walks on symmetric groups. 相似文献
2.
3.
4.
Mark Wildon 《Journal of Pure and Applied Algebra》2009,213(7):1464-1477
Building on work of Saxl, we classify the multiplicity-free permutation characters of all symmetric groups of degree 66 or more. A corollary is a complete list of the irreducible characters of symmetric groups (again of degree 66 or more) which may appear in a multiplicity-free permutation representation. The multiplicity-free characters in a related family of monomial characters are also classified. We end by investigating a consequence of these results for Specht filtrations of permutation modules defined over fields of prime characteristic. 相似文献
5.
The root systems appearing in the theory of Lie superalgebras and Nichols algebras admit a large symmetry extending properly
the one coming from the Weyl group. Based on this observation we set up a general framework in which the symmetry object is
a groupoid. We prove that in our context the groupoid is generated by simple reflections and Coxeter relations. In a broad
sense this answers a question of Serganova. Our weak version of the exchange condition allows us to prove Matsumoto’s theorem.
Therefore the word problem is solved for the groupoid. 相似文献
6.
Burkhard Külshammer Jorn B. Olsson Geoffrey R. Robinson 《Inventiones Mathematicae》2003,151(3):513-552
We study, via character-theoretic methods, an ℓ-analogue of the modular representation theory of the symmetric group, for
an arbitrary integer ℓ≥2. We find that many of the invariants of the usual block theory (ie. when ℓ is prime) generalize in
a natural fashion to this new context.
Oblatum 21-III-2002 & 5-VIII-2002?Published online: 8 November 2002 相似文献
7.
Craig J. Dodge 《Journal of Pure and Applied Algebra》2011,215(12):2949-2956
Let F be a field of characteristic p. We show that HomFΣn(Sλ,Sμ) can have arbitrarily large dimension as n and p grow, where Sλ and Sμ are Specht modules for the symmetric group Σn. Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks. 相似文献
8.
9.
D. Joyner 《Archiv der Mathematik》2003,81(2):113-120
The result here answers the following questions in the affirmative: Can
the Galois action on all abelian (Galois) fields $K/\mathbb{Q}$ be realized
explicitly via an action on characters of some finite group? Are all
subfields of a cyclotomic field of the form $\mathbb{Q}(\chi)$, for some
irreducible character $\chi$ of a finite group G? In particular, we
explicitly determine the Galois action on all irreducible characters of
the generalized symmetric groups. We also determine the smallest
extension of $\mathbb{Q}$ required to realize (using matrices) a given
irreducible representation of a generalized symmetric group.
Received: 18 February 2002 相似文献
10.
Anatol N. Kirillov 《Journal of Pure and Applied Algebra》2010,214(4):402-409
We give a model of the coinvariant algebra of the complex reflection groups as a subalgebra of a braided Hopf algebra called Nichols-Woronowicz algebra. 相似文献
11.
12.
Julia Weber 《Mathematische Zeitschrift》2007,256(1):57-74
We geometrically construct a homology theory that generalizes the Euler characteristic mod 2 to objects in the unoriented
cobordism ring of a topological space X. This homology theory Eh
* has coefficients in every nonnegative dimension. There exists a natural transformation that for X = pt assigns to each smooth manifold its Euler characteristic mod 2. The homology theory is constructed using cobordism of stratifolds,
which are singular objects defined below. An isomorphism of graded -modules is shown for any CW-complex X. For discrete groups G, we also define an equivariant version of the homology theory Eh
*, generalizing the equivariant Euler characteristic. 相似文献
13.
Nora Ganter 《Advances in Mathematics》2006,205(1):84-133
We generalize the definition of orbifold elliptic genus and introduce orbifold genera of chromatic level h, using h-tuples rather than pairs of commuting elements. We show that our genera are in fact orbifold invariants, and we prove integrality results for them. If the genus arises from an H∞-map into the Morava-Lubin-Tate theory Eh, then we give a formula expressing the orbifold genus of the symmetric powers of a stably almost complex manifold M in terms of the genus of M itself. Our formula is the p-typical analogue of the Dijkgraaf-Moore-Verlinde-Verlinde formula for the orbifold elliptic genus [R. Dijkgraaf et al., Elliptic genera of symmetric products and second quantized strings Comm. Math. Phys. 185(1) (1997) 197-209]. It depends only on h and not on the genus. 相似文献
14.
Koffi B. Fadimba 《Journal of Computational and Applied Mathematics》2010,234(1):272-282
We consider a linearization of a numerical scheme for the saturation equation (or porous medium equation) , through first order expansions of the fractional function f and the inverse of the function , after a regularization of the porous medium equation. We establish a regularity result for the Continuous Galerkin Method and a regularity result for the linearized scheme analogous to the corresponding nonlinear scheme. We then show that the linearized scheme is consistent with the nonlinear scheme analyzed in a previous work. 相似文献
15.
We construct a non-paracompact Hausdorff space for which ?ech cohomology does not coincide with sheaf cohomology. Moreover, the sheaf of continuous real-valued functions is neither soft nor acyclic, and our space admits non-numerable principal bundles. 相似文献
16.
Ken-Ichi Maruyama 《Topology》2007,46(3):319-341
We study nilpotent subgroups of automorphism groups in the category of groups and the homotopy category of spaces. We establish localization and completion theorems for nilpotent groups of automorphisms of nilpotent groups. We then apply these algebraic theorems to prove analogous results for certain groups of self-homotopy equivalences of spaces. 相似文献
17.
Ferran Cedó Tatiana Gateva-Ivanova Agata Smoktunowicz 《Journal of Pure and Applied Algebra》2018,222(12):3877-3890
We study left braces satisfying special conditions, or identities. We are particularly interested in the impact of conditions like Raut and lri on the properties of the left brace and its associated solution of the Yang–Baxter equation (YBE). We show that the solution of the YBE associated to the structure group (with the natural structure of a left brace) of a nontrivial solution of the YBE has multipermutation level 2 if and only if G satisfies lri. It is known that every (left) brace with lri satisfies condition Raut. We prove that for a graded Jacobson radical ring with no elements of additive order two the conditions lri and Raut are equivalent. We construct a finite two-sided brace with condition Raut which does not satisfy lri. We show that a finitely generated two-sided brace which satisfies lri has a finite multipermutation level which is bounded by the number of its generators. 相似文献
18.
A note on Cartan matrices for symmetric groups 总被引:2,自引:0,他引:2
Using generating functions, a very simple explicit formula for the
determinants of the p-Cartan matrices of symmetric groups is given.
Our method works also when p is a composite number.Received: 5 September 2001 相似文献
19.
Susanne C. Brenner 《Numerische Mathematik》1999,83(2):187-203
Summary. It is shown that for elliptic boundary value problems of order 2m the condition number of the Schur complement matrix that appears in nonoverlapping domain decomposition methods is of order
, where d measures the diameters of the subdomains and h is the mesh size of the triangulation. The result holds for both conforming and nonconforming finite elements.
Received: January 15, 1998 相似文献
20.
David Stanovský 《Algebra Universalis》2005,54(1):97-103
We study equational theories of several left symmetric left distributive operations on groups. Normal forms of terms in the
variety of LSLD groupoids, LSLD medial groupoids, LSLD idempotent groupoids and LSLD medial idempotent groupoids are found.
Received October 11, 2001; accepted in final form December 9, 2004. 相似文献