منابع مشابه
Twisted Symmetric Group Actions
Let K be any field, K(x1, . . . , xn) be the rational function field of n variables over K, and Sn and An be the symmetric group and the alternating group of degree n respectively. For any a ∈ K \ {0}, define an action of Sn on K(x1, . . . , xn) by σ · xi = xσ(i) for σ ∈ An and σ · xi = a/xσ(i) for σ ∈ Sn \ An. Theorem. For any field K and n = 3, 4, 5, the fixed field K(x1, . . . , xn) Sn is ra...
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This article is intended to answer the question “Why do you guys always want to twist everything?” We review the various ways in which twists, twisted actions and twisted crossed products arise, and then discuss some cohomological obstructions to the existence and triviality of twisted actions. Our review begins with the classical problems of classifying group extensions and irreducible unitary...
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Let X be a smooth, closed, connected spin 4-manifold with b1(X) = 0 and non-positive signature σ(X). In this paper we use Seiberg-Witten theory to prove that if X admits an odd type symmetric group S3 action preserving the spin structure, then b+2 (X) ≥ |σ(X)|/8 + 3 under some non-degeneracy conditions. We also obtain some information about IndS̃3 D, where S̃3 is the extension of S3 by Z2.
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We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group SN. The problem is closely related to the theory of characters and factor representations of gro...
متن کاملA Duality of the Twisted Group Algebra of the Symmetric Group and a Lie Superalgebra
The “character values” of the irreducible projective representations of Sk, the symmetric group of degree k, were determined by I. Schur using Schur’sQ-functions, which are indexed by the distinct partitions of k, [10], in a way analogous to Frobenius’ formula for the character values of the ordinary irreducible representations of Sk [2]. Behind Frobenius’ formula exists a duality relation of S...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2010
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2010.248.285