A Combinatorial Approach to Specht Module Cohomology
نویسندگان
چکیده
منابع مشابه
A Combinatorial Approach to Specht Module Cohomology
For a Specht module S for the symmetric group Σd, the cohomology H (Σd,S ) is known only in degree i = 0. We give a combinatorial criterion equivalent to the nonvanishing of the degree i = 1 cohomology, valid in odd characteristic. Our condition generalizes James’ solution in degree zero. We apply this combinatorial description to give some computations of Specht module cohomology, together wit...
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We introduce a way of describing cohomology of the symmetric groups Σn with coefficients in Specht modules. We study H (Σn, S λ R) for i ∈ {0, 1, 2} and R = Z, Fp. The focus lies on the isomorphism type of H(Σn, S λ Z ). Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of |H(Σn, S λ Z )|. The most important to...
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The wealth of beautiful combinatorics that arise in the representation theory of the symmetric group is well-known. In this paper, we analyze the representations of a related algebraic structure called the rook monoid from a combinatorial angle. In particular, we give a combinatorial construction of the irreducible representations of the rook monoid. Since the rook monoid contains the symmetric...
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ژورنال
عنوان ژورنال: Algebra Colloquium
سال: 2012
ISSN: 1005-3867,0219-1733
DOI: 10.1142/s1005386712000661