Let p be an odd prime and let n be a natural number. In this article we determine the irreducible constituents of the permutation module induced by the action of the symmetric group Sn on the cosets ...of a Sylow p-subgroup Pn. As a consequence, we determine the number of irreducible representations of the corresponding Hecke algebra H(Sn,Pn,1Pn).
In 2012 Raghavan, Samuel, and Subrahmanyam showed that the Kazhdan–Lusztig basis for the Iwahori–Hecke algebra in type A provides a “canonical” basis for the centraliser algebra of the Schur algebra ...acting on tensor space. In 2022 the second author found a similar result for the centraliser of the partition algebra acting on the same tensor space. Each basis is indexed by permutations. We exploit these bases to show that the linear decomposition of an arbitrary invariant (in either centraliser algebra) depends integrally on its entries, and describe combinatorial rules that pick out minimal sets of such entries.
We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In ...many of the still open cases small upper bounds are found.
We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This provides an explanation of the stability ...properties of plethysm and Kronecker coefficients in a simple and uniform fashion for the first time. We prove the strengthened Foulkes' conjecture for stable plethysm coefficients in an elementary fashion.
Over fields of characteristic 2, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and ...a closed formula for the dimension of their endomorphism algebra remain two important open problems in the area. In this paper, we introduce a novel description of the endomorphism algebra of the Specht modules and provide infinite families of Specht modules with one-dimensional endomorphism algebra.
Let p be a prime greater than 3. In this paper we showed that a nonsolvable transitive permutation group of degree p containing an odd permutation is equal to the symmetric group Sp. This answered ...the question proposed by Ito (1963) 8. Then we studied the generators of Sp and gave the number of rotary maps up to isomorphism. The rotary maps here are of valency p and have automorphism group Sp.
•Answers Ito's question proposed in 1963.•Generators of Sp: Using our findings, we delved into the generators of the symmetric group Sp.•Determined the number of a family of rotary maps up to isomorphism.
Applications on Cyclic Soft Symmetric Groups Mahmood Khalil, Shuker; Hameed Khadhaer, Fatima
Journal of physics. Conference series,
05/2020, Letnik:
1530, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In classical groups, there is a fact state that the symmetric groups are not cyclic in general. So, in this work the notion of cyclic soft symmetric groups using soft set theory is investigated and ...their orders are given. In this paper, we introduce new classes over non cyclic symmetric groups; these new classes are generated by element in the power set of classical symmetric groups. Furthermore, some applications on these new classes are given.
We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting of the classes that naturally arise from the Białynicki-Birula decomposition of the Hessenberg ...varieties. We give an explicit combinatorial description of the support of each class, which enables us to compute the symmetric group actions on the classes in our bases. We then successfully apply the results to the permutohedral varieties to explicitly write down each class and to construct permutation submodules that constitute summands of a decomposition of cohomology space of each degree. This resolves the problem posed by Stembridge on the geometric construction of permutation module decomposition and also the conjecture posed by Chow on the construction of bases for the equivariant cohomology spaces of permutohedral varieties.
PDF
