Kronecker Products of sn-Characters in Hooks
نویسندگان
چکیده
منابع مشابه
A Stability Property for Coefficients in Kronecker Products of Complex Sn Characters
In this note we make explicit a stability property for Kronecker coefficients that is implicit in a theorem of Y. Dvir. Even in the simplest nontrivial case this property was overlooked despite of the work of several authors. As applications we give a new vanishing result and a new formula for some Kronecker coefficients.
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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...
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We present new expressions for generating functions of irreducible characters of the symmetric group Sn. These generating functions are of the form ∑∗ λ χ λ μq λ where the sum is over partitions λ of restricted shapes such as hooks and double hooks. We use the λ-ring theory for symmetric functions to demonstrate our statements.
متن کاملOn (almost) Extreme Components in Kronecker Products of Characters of the Symmetric Groups
Using a recursion formula due to Dvir, we obtain information on maximal and almost maximal components in Kronecker products of characters of the symmetric groups. This is applied to confirm a conjecture made by Bessenrodt and Kleshchev in 1999, which classifies all such Kronecker products with only three or four components.
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: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8976