Higher Specht polynomials for the symmetric group
نویسندگان
چکیده
منابع مشابه
Symmetric Group Modules with Specht and Dual Specht Filtrations
The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group theory analogous to that of good filtrations and tilting modules for GLn(k). This paper is an initial attempt at such a theory. We obtain two sufficient conditi...
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During the 2004-2005 academic year the VIGRE algebra research group at the University of Georgia computed the complexities of certain Specht modules S for the symmetric group Σd, using the computer algebra program Magma. The complexity of an indecomposable module does not exceed the p-rank of the defect group of its block. The Georgia group conjectured that, generically, the complexity of a Spe...
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This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A corollary of this theorem is a new way to determine the defect groups of symmetric groups. The main theorem is also used to find the Green correspondents of...
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A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N − 2, 1, 1) of the symmetric group SN for odd N and parameter values − 1 2 ,− 3 2 ,...
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An explicit formula for the chromatic polynomials of certain families of graphs, called ‘bracelets’, is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads to an effective means of calculation. MSC 2000: 05C15, 05C50.
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1993
ISSN: 0386-2194
DOI: 10.3792/pjaa.69.41