Stanley’s Formula for Characters of the Symmetric Group
نویسندگان
چکیده
منابع مشابه
An explicit formula for the characters of the symmetric group
The characters of the irreducible representations of the symmetric group play an important role in many areas of mathematics. However, since the early work of Frobenius [5] in 1900, no explicit formula was found for them. The characters of the symmetric group were computed through various recursive algorithms, but explicit formulas were only known for about ten particular cases [5, 9]. The purp...
متن کاملThe characters of the symmetric group.
A short and simple derivation of the formula of Frobenius, which gives the dimensions of the irreducible representations of S(n), the symmetric group on any number, n, of symbols, is given. These dimensions are the characters of the identity element of the group, i.e., of the element all of whose cycles are unary. It is shown how a slight modification of Frobenius' formula yields, when n = 2p i...
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Following the work of B. Külshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the l-defect of characters of the symmetric group Sn, where l > 1 is an arbitrary integer. We prove that the l-defect is given by an analogue of the hook-length formula, and use it to prove, when n < l, an l-version of the McKay Conjecture in Sn.
متن کاملGeneralized Characters of the Symmetric Group
Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...
متن کاملCharacters and Inversions in the Symmetric Group
We consider sums of the form π∈Sn χ λ/µ (π) q inv(π) where χ λ/µ is a skew character of the symmetric group and inv(π) is the number of inversions of π. Our main result gives a lower bound on the number of factors of 1 + q and 1 − q which divide the above sum, and is shown to be sharp when λ/µ is a hook partition shape. Résumé Nous considérons des sommes de la forme
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2010
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-009-0038-5