Kronecker products, characters, partitions, and the tensor square conjectures
نویسندگان
چکیده
منابع مشابه
Kronecker Products, Characters, Partitions, and the Tensor Square Conjectures
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups Sn contain all irreducibles as their constituents. Our main result is that they contain representations corresponding to hooks and two row Young diagrams. For that, we develop a new sufficient condition for the positivity of Kronecker coefficients in terms of c...
متن کاملKronecker coefficients: the tensor square conjecture and unimodality
We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the Sn-irreducible representation indexed by the staircase partition contains every irreducible representation of Sn. We present a sufficient condition allowing to determine whether an irreducible representation is...
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The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorisation operations and the commutation...
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Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...
متن کاملOn Kronecker Products of Spin Characters of the Double Covers of the Symmetric Groups
In recent years, a number of results on Kronecker products of complex Sncharacters have been obtained. In particular, the rectangular hull for the constituents in such products was found, and this was used for the classification of products with few homogeneous components; see [1] for this classification result and references to related work. Here, we provide similar results for products of spi...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2016
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.11.002