171,832 research outputs found
On the structure of Foulkes modules for the symmetric group
No full textThis thesis concerns the structure of Foulkes modules for the symmetric group. We study `ordinary' Foulkes modules , where and are natural numbers, which are permutation modules arising from the action on cosets of . We also study a generalisation of these modules , labelled by a partition of , which we call generalised Foulkes modules.
Working over a field of characteristic zero, we investigate the module structure using semistandard homomorphisms. We identify several new relationships between irreducible constituents of and , where is a natural number, and also apply the theory to twisted Foulkes modules, which are labelled by , obtaining analogous results.
We make extensive use of character-theoretic techniques to study , the ordinary character afforded by the Foulkes module , and we draw conclusions about near-minimal constituents of in the case where is even. Further, we prove a recursive formula for computing character multiplicities of any generalised Foulkes character , and we decompose completely the character in the cases where has either two rows or two columns, or is a hook partition.
Finally, we examine the structure of twisted Foulkes modules in the modular setting. In particular, we answer questions about the structure of over fields of prime characteristic
Generalized Foulkes' Conjecture and Tableaux Construction
No full textFoulkes conjectured that for n=ab and a ≤ b, every irreducible module occurring as a constituent in 1Sb∫SaSn occurs with greater or equal multiplicity in 1Sa∫SbSn. We generalize part of this to say those irreducibles also occur in 1Sd∫ScSn, where cd=n and c,d ≥ a. We prove the generalized conjecture for a=2 and a=3, by explicitly constructing the corresponding tableaux. We also prove the multiplicity constraint for certain cases. For these proofs we develop a theory of construction conditions for tableaux giving rise to Sb∫Sa modules and in doing so, completely classify all such tableaux for a=2 and a=3
Minimal and maximal constituents of twisted Foulkes characters
No full textWe prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric group that generalize Foulkes permutation characters. Restated in the language of symmetric functions, our results determine all minimal and maximal partitions that label Schur functions appearing in the plethysms . As a corollary we prove
two conjectures of Agaoka on the lexicographically least constituents of the plethysms and
The fish circadian timing system: The illuminating case of light-responsive peripheral clocks [*Pagano C. first author]
No full textStudying the Evolution of the Vertebrate Circadian Clock
No full textThe utility of any model species cannot be judged solely in terms of the tools and approaches it provides for genetic analysis. A fundamental consideration is also how its biology has been shaped by the environment and the ecological niche which it occupies. By comparing different species occupying very different habitats we can learn how molecular and cellular mechanisms change during evolution in order to optimally adapt to their environment. Such knowledge is as important as understanding how these mechanisms work. This is illustrated by the use of fish models for studying the function and evolution of the circadian clock. In this review we outline our current understanding of how fish clocks sense and respond to light and explain how this differs fundamentally from the situation with mammalian clocks. In addition, we present results from comparative studies involving two species of blind cavefish, Astyanax mexicanus and Phreatichthys andruzzii. This work reveals the consequences of evolution in perpetual darkness for the circadian clock and its regulation by light as well as for other mechanisms such as DNA repair, sleep, and metabolism which directly or indirectly are affected by regular exposure to sunlight. Major differences in the cave habitats inhabited by these two cavefish species have a clear impact on shaping the molecular and cellular adaptations to life in complete darkness
On a Conjecture of Foulkes
No full textAbstractSuppose that Ω={1,2,…,ab} for some non-negative integers a and b. Denote by P(a,b) the set of unordered partitions of Ω into a parts of cardinality b. In this paper we study the decomposition of the permutation module CP(a,b) where C is the field of complex numbers. In particular, we show that CP(3,b) is isomorphic to a submodule of CP(b,3) for b≥3. This settles the next unproven case of a conjecture of Foulkes
Foulkes (S.), Kadis (A.l.), Krasner (J.D.) Et Winick (C.). — Guide du psychothérapeute de groupe. Epi, Paris, 1971
No full textTurbiaux Marcel. Foulkes (S.), Kadis (A.l.), Krasner (J.D.) Et Winick (C.). — Guide du psychothérapeute de groupe. Epi, Paris, 1971. In: Bulletin de psychologie, tome 25 n°296, 1972. pp. 370-371
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows
No full textWe 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. To show this, we construct a new algorithm for computing cocyclage in terms of which the conjecture is described. Our algorithm is free of local constraints, which were the main obstacle in Lecouvey's original construction. In particular, we show that our model is governed by the situation in type A. This approach works for arbitrary weight and we expect it to lead to a proof of the conjecture in full generality. (C) 2020 The Author(s). Published by Elsevier Inc.GR-TE
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