Foulkes conjecture

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August undefined, 2024

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 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). WebFoulkes’ conjecture (see (2.1)) for a new in nite family of cases, see Theorem 3.5. 2 Representation theoretic obstructions In this section we review how to separate group varieties via representation theoretic multiplicities. The setup is in complete analogy to the geometric complexity theory approach of Mulmuley and Sohoni.

(PDF) A q-Analog of Foulke

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 ... 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. needs in github workflow

Foulkes modules and decomposition numbers of the symmetric …

WebMar 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 ) … WebThe original Foulkes‘ conjecture, which dates back to 1949, was stated as a “theorem” (at page 206 of paper) but with no claim that there actually was a proof.As it is, more than … Webties to conjecture 3, we rapidly recall some properties and specializations of the symmetric polynomials H µ ( x ; q , t ). 2 Howev er, it is not clear in [ 9 ] where this exact statement can be ... itf fortnite item shop

Stable properties of plethysm : on two conjectures of Foulkes

Foulkes conjecture

On geometric complexity theory: Multiplicity obstructions are …

WebJan 28, 2024 · The Kostka–Foulkes polynomials $K_{\lambda \mu }(t)$ associated with a pair of partitions $\lambda , \mu $ have figured prominently in representation theory and algebraic combinatorics (cf. [1, 14]).They have arisen in the context of character theory of the general linear group over the finite field [] in terms of the Hall–Littlewood polynomials []. 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].

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WebNov 22, 2024 · [Fou50] H. O. Foulkes. Concomitants of the quintic and sextic up to degree four in the coefficients of the ground form. Journal of the London Mathematical Society, s1-25 (3):205–209, July 1950. [GV85] Ira Gessel and Gérard Viennot. Binomial determinants, paths, and hook length formulae. Advances in Mathematics, 58 (3):300–321, December … WebJan 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) …

WebThe long-standing Foulkes' Conjecture asserts that a certain difference of plethythms of complete homogeneous symmetric functions is Schur-positive. Vessenes has stated a … WebApr 6, 2024 · The Gaussian inequality is proven for multicomponent rotators with negative correlations between two spin components. In the case of one-component systems, the Gaussian inequality is shown to be a ...

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 … WebSep 13, 2015 · The Foulkes conjecture states that the multiplicities in the plethysm Sym^a(Sym^b V) are at most as large as the multiplicities in the plethysm Sym^b(Sym^a V) for all a <= b. This conjecture has ...

WebWe describe how certain permutation actions of large symmetric groups can be efficiently implemented on a computer. Using a specially tailored adaptation of a general technique to enumerate huge orbits and substantial distributed computation on a cluster of …

WebOn Foulkes’ conjecture William F. Doran IV * Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA Communicated by P.J. Freyd; … itf freightWebFeb 1, 2012 · These results generalize the Murnaghan--Nakayama rule and special cases of the Littlewood--Richardson rule. As a corollary we obtain a new combinatorial formula for the character multiplicities that are the subject of the long-standing Foulkes' Conjecture. Using this formula we verify Foulkes' Conjecture in some new cases. itf fortniteWebApr 1, 2000 · There is an extensive literature on the conjecture of Foulkes. In [1] Black and List show that the map ψ (b a ) : H (b a ) → H (a b ) is injective when a = 2 and b a. needs jigsaw social workWebExpanding 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 plethysm ... needs in tagalogWebExpanding 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 … itf france 08aWebMay 1, 2024 · The Foulkes conjecture states that the multiplicities in the plethysm Sym a (Sym b V) are at most as large as the multiplicities in the plethysm Sym b (Sym a V) for … need sizeWebThis 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. itf fortnite item shop today