On symmetric functions and the spin characters of
John R. Stembridge (1990)
Banach Center Publications
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John R. Stembridge (1990)
Banach Center Publications
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Michał Lorens (1980)
Annales Polonici Mathematici
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Kyong T. Hahn, Josephine Mitchell (1973)
Annales Polonici Mathematici
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Emmanuel Letellier (2013)
Journal of the European Mathematical Society
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Given a tuple of irreducible characters of we define a star-shaped quiver together with a dimension vector . Assume that is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied,...
Naotsugu Chinen (2015)
Commentationes Mathematicae Universitatis Carolinae
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By , , we denote the -th symmetric product of a metric space as the space of the non-empty finite subsets of with at most elements endowed with the Hausdorff metric . In this paper we shall describe that every isometry from the -th symmetric product into itself is induced by some isometry from into itself, where is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence...
Jan Waszkiewicz (1973)
Colloquium Mathematicae
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E. Karapınar, M. Yurdakul, V. Zahariuta (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let ℓ be a Banach sequence space with a monotone norm , in which the canonical system is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products where and are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by...
Gordon James (1990)
Banach Center Publications
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S.Yu. Orevkov (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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For the groups , , , over a finite field we solve the class product problem, i.e., we give a complete list of -tuples of conjugacy classes whose product does not contain the identity matrix.
Brenda Johnson, Randy McCarthy (2008)
Fundamenta Mathematicae
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We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, and , in terms of the first terms in the Taylor towers of and for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of and . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for and .
Hajime Kaneko, Takeshi Kurosawa, Yohei Tachiya, Taka-aki Tanaka (2015)
Acta Arithmetica
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Let d ≥ 2 be an integer. In 2010, the second, third, and fourth authors gave necessary and sufficient conditions for the infinite products (i=1,...,m) or (i=1,...,m) to be algebraically dependent, where are non-zero integers and and are generalized Fibonacci numbers and Lucas numbers, respectively. The purpose of this paper is to relax the condition on the non-zero integers to non-zero real algebraic numbers, which gives new cases where the infinite products above are algebraically...
Yves Benoist, Toshiyuki Kobayashi (2015)
Journal of the European Mathematical Society
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Let be a semisimple algebraic Lie group and a reductive subgroup. We find geometrically the best even integer for which the representation of in is almost . As an application, we give a criterion which detects whether this representation is tempered.
Bo'az Klartag (2010)
Journal of the European Mathematical Society
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Suppose that is an absolutely continuous probability measure on n, for large . Then has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if , then there exist -dimensional marginals of that are -far from being sphericallysymmetric, in an appropriate sense. Here is a universal constant.
Sandra Rozensztajn (2014)
Journal de Théorie des Nombres de Bordeaux
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We study the irreducible constituents of the reduction modulo of irreducible algebraic representations of the group for a finite extension of . We show that asymptotically, the multiplicity of each constituent depends only on the dimension of and the central character of its reduction modulo . As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-Mézard conjecture.
Martin Liebeck, Dan Segal, Aner Shalev (2012)
Journal of the European Mathematical Society
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For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded). ...
K. Orlov (1980)
Matematički Vesnik
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Ju-Lee Kim (2004)
Bulletin de la Société Mathématique de France
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Let be a -adic field. Let be the group of -rational points of a connected reductive group defined over , and let be its Lie algebra. Under certain hypotheses on and , wethe tempered dual of via the Plancherel formula on , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on and . As a consequence, we prove that any tempered representation contains a good minimal -type; we extend this result to irreducible...
Joshua Harrington, Lenny Jones (2013)
Colloquium Mathematicae
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Let , where . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of on the coefficients of f(x) is the best possible in this situation.