Foulkes conjecture
WebWe show that Foulkes' first conjecture holds forn large enough with respect tom (Corollary 1.3). Moreover, we state and prove two broad generalizations of Foulkes' second … WebThis defect theory can unify some well known results in modular representation theory. By using generalized Schur's lemma, we can also give a method to determine the multiplicity of simple modules in any permutation module of symmetric groups. This makes it possible to prove various versions of Foulkes' conjecture in a uniform way.
Foulkes conjecture
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S. H. Foulkes was a German-British psychiatrist and psychoanalyst. He developed a theory of group behaviour that led to his founding of group analysis, a variant of group therapy. He initiated the Group Analytic Society, and the Institute of Group Analysis (IGA) in London. In 1933, owing to his Jewish descent, Foulkes emigrated to England. In 1938, he was granted British citizenship and changed his name to S. H. Foulkes. WebFeb 1, 2015 · In characteristic zero, the module H (2 m) arises in the first non-trivial case of Foulkes' Conjecture (see [17]). For this reason we call H (2 m) a Foulkes module and H (2 m; k) a twisted Foulkes module. For some recent results on the characters of general Foulkes modules we refer the reader to [18] and [35].
WebUsing a specially tailored adaptation of a general technique to enumerate huge orbits and substantial distributed computation on a cluster of workstations, further evidence related to the approach to Foulkes' conjecture is collected. We describe how certain permutation actions of large symmetric groups can be efficiently implemented on a computer. WebA Zero-Multiplicity Problem Related to Foulkes' Conjecture. Ask Question Asked 8 years, 7 months ago. Modified 6 years, 8 months ago. Viewed 769 times 8 $\begingroup$ I'm a combinatorialist that is interested in estimating multiplicities of irreps of $1^{S_{kn}}_{S_k \wr S_n}$ (the action of symmetric group on uniform partitions). ...
Web3-parameter special case of Conjecture 1 which we dubbed the β-Conjecture. Namely, Conjecture 3. For integers 0 < a < b and β ≥ 1, we have b +βa b q ≥ a+βb a q. (3) The case β = 1 is trivial. However, our journey in this effort failed short of capturing the β-Conjecture in its fullest. In the sequel, we supply the details of our ... WebFeb 25, 2016 · We propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n ...
Web3-parameter special case of Conjecture 1 which we dubbed the β-Conjecture. Namely, Conjecture 3. For integers 0 < a < b and β ≥ 1, we have b +βa b q ≥ a+βb a q. (3) The …
WebIn 1950, Foulkes while analysing the structure of F n m for some speci c mand n observed that Fm n can be embedded in F n m when m british wartime recipesWebConjecture 1.1. [Foulkes 50] Let m,n ∈ N with m ≥ n. Then the permutation module QΩm,n is a QSmn-submodule of the permutation module QΩn,m. In Section 2, we describe how … capital markets. cfiWebSep 1, 2024 · We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka–Foulkes polynomials, in the case of rows of arbitrary weight. british wastelands crossword clueWebJan 15, 2015 · When the field K is the field of complex numbers C, the study of the decomposition into irreducible direct summands of the Foulkes module is closely related to the problem known as Foulkes' Conjecture as stated firstly in [7] by H.O. Foulkes in 1950. Conjecture. Let K = C and let a and n be natural numbers such that a < n. Then H (n a) … capital markets consultants drew horterWebMar 1, 2008 · The Siemons, Wagner and Stanley (SWS) Conjecture is related to an earlier conjecture by Foulkes [6] that there exists an injective FG-homomorphism H (b a ) arrowhookleft→ H (a b ) when a lessorequalslant b. When a lessorequalslant 3 this conjecture has been shown to be true by Dent and Siemons [5]. capital markets cottonwood reitWebExpanding Foulkes conjecture to more general diagrams 8. 6. Experimental data for the q-diagram ex pansion 10. 7. F rom diagram Foulkes to diagram q-Foulkes 11. 8. Iterated … british washroomWebWe show that Foulkes' first conjecture holds forn large enough with respect tom (Corollary 1.3). Moreover, we state and prove two broad generalizations of Foulkes' second conjecture. They hold in the framework of representations of connected reductive groups, and they lead e.g. to a general analog of Hermite's reciprocity law (Corollary 1 in 3.3). capital markets crc limited