Representations of $S_n$ and $GL_n$ and the q-Schur algebra

Gordon James

Displaying similar documents to “Representations of $S_{n}$ and $G L_{n}$ and the q-Schur algebra”

The correspondence between Barsotti-Tate groups and Kisin modules when $p = 2$

Tong Liu (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $K$ be a finite extension over $ℚ_{2}$ and $𝒪_{K}$ the ring of integers. We prove the equivalence of categories between the category of Kisin modules of height 1 and the category of Barsotti-Tate groups over $𝒪_{K}$ .

The density of representation degrees

Martin Liebeck, Dan Segal, Aner Shalev (2012)

Journal of the European Mathematical Society

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For a group $G$ and a positive real number $x$ , define $d_{G} (x)$ to be the number of integers less than $x$ which are dimensions of irreducible complex representations of $G$ . We study the asymptotics of $d_{G} (x)$ for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups $G$ in characteristic zero, showing that either there exists $α > 0$ such that $d_{G} (x) > x^{α}$ for all large $x$ , or $G$ is virtually abelian (in which case $d_{G} (x)$ is bounded). ...

Tempered reductive homogeneous spaces

Yves Benoist, Toshiyuki Kobayashi (2015)

Journal of the European Mathematical Society

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Let $G$ be a semisimple algebraic Lie group and $H$ a reductive subgroup. We find geometrically the best even integer $p$ for which the representation of $G$ in $L^{2} (G / H)$ is almost $L^{p}$ . As an application, we give a criterion which detects whether this representation is tempered.

Products of conjugacy classes in finite unitary groups $G U (3, q^{2})$ and $S U (3, q^{2})$

S.Yu. Orevkov (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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For the groups $G U (3)$ , $S U (3)$ , $G L (3)$ , $S U (3)$ over a finite field we solve the class product problem, i.e., we give a complete list of $m$ -tuples of conjugacy classes whose product does not contain the identity matrix.

Entropy of Schur–Weyl measures

Sevak Mkrtchyan (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Relative dimensions of isotypic components of $N$ th order tensor representations of the symmetric group on $n$ letters give a Plancherel-type measure on the space of Young diagrams with $n$ cells and at most $N$ rows. It was conjectured by G. Olshanski that dimensions of isotypic components of tensor representations of finite symmetric groups, after appropriate normalization, converge to a constant with respect to this family of Plancherel-type measures in the limit when $\frac{N}{\sqrt{n}}$ converges to a constant....

Product decompositions of quasirandom groups and a Jordan type theorem

Nikolay Nikolov, László Pyber (2011)

Journal of the European Mathematical Society

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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If $k$ is the minimal degree of a representation of the finite group $G$ , then for every subset $B$ of $G$ with $| B | > | G | / k^{1 / 3}$ we have $B^{3} = G$ . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if $k \geq 2$ , then $G$ has a...

On the structural theory of ${II}_{1}$ factors of negatively curved groups

Ionut Chifan, Thomas Sinclair (2013)

Annales scientifiques de l'École Normale Supérieure

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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor $L Γ$ is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that $L Γ$ is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in $Sp (n, 1)$ , $n \geq 2$ , are virtually $W^{*}$ -superrigid.

A representation theorem for $(X_{1} - 1) (X_{2} - 1) . . . (X_{n} - 1)$ and its applications

D. Ž. Djoković (1969)

Annales Polonici Mathematici

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Localization techniques in $L^{p}$ spaces

A. Pełczyński, H. Rosenthal (1975)

Studia Mathematica

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The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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On C $^{*}$ -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

Annales Polonici Mathematici

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On the $p^{λ}$ problem

Stephan Baier (2004)

Acta Arithmetica

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An explicit computation of $p$ -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we give a concrete method to compute $p$ -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over $p$ -adic fields. An application to the global setting is also discussed. In particular, we give an explicit $p$ -stabilized form of a Saito-Kurokawa lift.

On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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Геометрическая теория состояний, граница фон Неймана, двойственность $C^{*}$ -алгерб

А.М. Вершик (1972)

Zapiski naucnych seminarov Leningradskogo

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Displaying similar documents to “Representations of S n and G L n and the q-Schur algebra”

Displaying similar documents to “Representations of $S_{n}$ and $G L_{n}$ and the q-Schur algebra”