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1.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2007,259(2):S12-S34
The investigation of the pairs of irreducible characters of the symmetric group S n that have the same set of roots in one of the sets A n and S n ? A n is continued. All such pairs of irreducible characters of the group S n are found in the case when the least of the main diagonal’s lengths of the Young diagrams corresponding to these characters does not exceed 2. Some arguments are obtained for the conjecture that alternating groups A n have no pairs of semiproportional irreducible characters. 相似文献
2.
Christine Bessenrodt 《Archiv der Mathematik》2007,89(1):1-9
Starting from the question when all irreducible p-Brauer characters for a symmetric or an alternating group are of p-power degree, we classify the p-modular irreducible representations of p-power dimension in some families of representations for these groups. In particular, this then allows to confirm a conjecture
by W. Willems for the alternating groups.
Received: 14 June 2006 相似文献
3.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
4.
Lingli Wang 《Frontiers of Mathematics in China》2010,5(1):179-190
Let G be a finite group, and let π
e
(G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M). In this short paper, we prove that if G is a finite group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M), where M = D
n
(2) and n is even. 相似文献
5.
Lower estimates for the maximal weight multiplicities in irreducible representations of the algebraic groups of type C
n
in characteristic p ≤ 7 are found. If n ≥ 8 and p ≠ 2 , then for an irreducible representation either such a multiplicity is at least n− 4 − [n]4,where [n]4 is the residue of n modulo 4, or all the weight multiplicities are equal to 1.For p = 2, the situation is more complicated, and for every n and l there exists a class of representations with the maximal weight multiplicity equal to 2
l
. For symplectic groups in characteristic p > 7 and spinor groups similar results were obtained earlier. Bibliography: 15 titles. 相似文献
6.
We prove that a 2-group has exactly five rational irreducible characters if and only if it is dihedral, semidihedral or generalized quaternion. For an arbitrary prime p, we say that an irreducible character χ of a p-group G is “almost rational” if ℚ(χ) is contained in the cyclotomic field ℚ p , and we write ar(G) to denote the number of almost-rational irreducible characters of G. For noncyclic p-groups, the two smallest possible values for ar(G) are p 2 and p 2 + p − 1, and we study p-groups G for which ar(G) is one of these two numbers. If ar(G) = p 2 + p − 1, we say that G is “exceptional”. We show that for exceptional groups, |G: G′| = p 2, and so the assertion about 2-groups with which we began follows from this. We show also that for each prime p, there are exceptional p-groups of arbitrarily large order, and for p ≥ 5, there is a pro-p-group with the property that all of its finite homomorphic images of order at least p 3 are exceptional. 相似文献
7.
In this paper we consider n-poised planar node sets, as well as more special ones, called G C n sets. For the latter sets each n-fundamental polynomial is a product of n linear factors as it always holds in the univariate case. A line ? is called k-node line for a node set \(\mathcal X\) if it passes through exactly k nodes. An (n + 1)-node line is called maximal line. In 1982 M. Gasca and J. I. Maeztu conjectured that every G C n set possesses necessarily a maximal line. Till now the conjecture is confirmed to be true for n ≤ 5. It is well-known that any maximal line M of \(\mathcal X\) is used by each node in \(\mathcal X\setminus M, \)meaning that it is a factor of the fundamental polynomial. In this paper we prove, in particular, that if the Gasca-Maeztu conjecture is true then any n-node line of G C n set \(\mathcal {X}\) is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes. We prove also similar statements concerning n-node or (n ? 1)-node lines in more general n-poised sets. This is a new phenomenon in n-poised and G C n sets. At the end we present a conjecture concerning any k-node line. 相似文献
8.
A finite group G is called p
i
-central of height k if every element of order p
i
of G is contained in the k
th
-term ζ
k
(G) of the ascending central series of G. If p is odd, such a group has to be p-nilpotent (Thm. A). Finite p-central p-groups of height p − 2 can be seen as the dual analogue of finite potent p-groups, i.e., for such a finite p-group P the group P/Ω1(P) is also p-central of height p − 2 (Thm. B). In such a group P, the index of P
p
is less than or equal to the order of the subgroup Ω1(P) (Thm. C). If the Sylow p-subgroup P of a finite group G is p-central of height p − 1, p odd, and N
G
(P) is p-nilpotent, then G is also p-nilpotent (Thm. D). Moreover, if G is a p-soluble finite group, p odd, and P ∈ Syl
p
(G) is p-central of height p − 2, then N
G
(P) controls p-fusion in G (Thm. E). It is well-known that the last two properties hold for Swan groups (see [11]). 相似文献
9.
V. O. Pekhterev 《Ukrainian Mathematical Journal》2009,61(9):1467-1474
We study the structure of the semigroup OT
n
, which is a unique (up to an isomorphism) R-section of the semigroup T
n
. For this semigroup, we describe Green relations, determine regular and nilpotent elements, describe maximal nilpotent subsemigroups,
and determine the unique irreducible system of generatrices and maximal subsemigroups. 相似文献
10.
V. S. Atabekyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(5):237-242
There is a well-known fact, that any group G
1 is a CEP-subgroup both for the direct product G
1 × G
2 and the free productG
1 * G
2 of G
1 with any group G
2. The paper gives a necessary and sufficient condition providing that a multiplier G
i
of a n-periodic product Π
i∈I
n
G
i
of any family of groups {G
i
}
i∈I
is a CEP-subgroup. Particularly, the found criterionmeans that any group G
1 of odd period n ≥ 665 is a CEP-subgroup of the n-periodic product Π
i∈I
n
G
i
for any group G
2. 相似文献
11.
Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B
sG
the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and B∩T ≤ B
sG
. A subgroup L of G is called a quaternionic subgroup whenever G has a section A/B isomorphic to the order 8 quaternion group such that L ≤ A and L ∩ B = 1. This article is devoted to proving the following theorem. 相似文献
12.
In Combinatorica 17(2), 1997, Kohayakawa, ?uczak and Rödl state a conjecture which has several implications for random graphs. If the conjecture is true, then, for example, an application of a version of Szemerédi’s regularity lemma for sparse graphs yields an estimation of the maximal number of edges in an H-free subgraph of a random graph G n, p . In fact, the conjecture may be seen as a probabilistic embedding lemma for partitions guaranteed by a version of Szemerédi’s regularity lemma for sparse graphs. In this paper we verify the conjecture for H = K 4, thereby providing a conceptually simple proof for the main result in the paper cited above. 相似文献
13.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
14.
A new functor from <Emphasis Type="Italic">D</Emphasis><Subscript>5</Subscript>-Mod to <Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript>-Mod
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Xiao Ping Xu 《数学学报(英文版)》2016,32(8):867-892
We find a new representation of the simple Lie algebra of type E 6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen’s idea of mixed product, we construct a new functor from D 5-Mod to E 6-Mod. A condition for the functor to map a finite-dimensional irreducible D 5-module to an infinite-dimensional irreducible E 6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant’s characteristic identities plays a key role. 相似文献
15.
A subgroup H of a finite group G is said to be c*-supplemented in G if there exists a subgroup K such that G = HK and H ⋂ K is permutable in G. It is proved that a finite group G that is S
4-free is p-nilpotent if N
G
(P) is p-nilpotent and, for all x ∈ G\N
G
(P), every minimal subgroup of
is c*-supplemented in P and (if p = 2) one of the following conditions is satisfied: (a) every cyclic subgroup of
of order 4 is c*-supplemented in P, (b)
, (c) P is quaternion-free, where P a Sylow p-subgroup of G and
is the p-nilpotent residual of G. This extends and improves some known results.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1011–1019, August, 2007. 相似文献
16.
The simple group A
1(p
n
) is proved to be uniquely determined by the set of the orders of the maximal abelian subgroups of A
1(p
n
). 相似文献
17.
Benny Sudakov 《Combinatorica》2007,27(4):509-518
We show that every K
4-free graph G with n vertices can be made bipartite by deleting at most n
2/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with
parts of size n/3. This proves an old conjecture of P. Erdős.
Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred
P. Sloan fellowship. 相似文献
18.
We show that for every odd integer p 1 there is an absolute positive
constantcp, so that the maximum cardinality of a set of vectors in Rn
such that the lp distance between
any pair is precisely 1, is at most cp
n log n.
We prove some upper bounds for other lp norms as well. 相似文献
19.
We prove that if ap-groupA acts on a solvablep′-groupG then there is a “large” orbit on the ordinary complex irreducible characters ofG. As a consequence of this theorem we obtain results that relate ordinary and Brauer character degrees.
Research supported by the FEDER, the Spanish Ministerio de Ciencia y Tecnología, grant BFM2001-0180, and Programa Ramón y
Cajal. 相似文献
20.
P. P. Nikitin 《Journal of Mathematical Sciences》2007,141(4):1479-1493
We consider the walled Brauer algebra Br
k, l(n) introduced by V. Turaev and K. Koike. We prove that it is a subalgebra of the Brauer algebra and that it is isomorphic,
for sufficiently large n ∈ ℕ, to the centralizer algebra of the diagonal action of the group GLn(ℂ) in a mixed tensor space. We also give the presentation of the algebra Br
k, l(n) by generators and relations. For a generic value of the parameter, the algebra is semisimple, and in this case we describe
the Bratteli diagram for this family of algebras and give realizations for the irreducible representations. We also give a
new, more natural proof of the formulas for the characters of the walled Brauer algebras. Bibliography: 29 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 170–198. 相似文献