Symmetric group characters as symmetric functions
نویسندگان
چکیده
We introduce a basis of the symmetric functions that evaluates to (irreducible) characters group, just as Schur evaluate irreducible G L n modules. Our main result gives three different characterizations for this basis. One shows structure coefficients (outer) product these are stable Kronecker coefficients. The results in paper focus on developing fundamental properties
منابع مشابه
Characters 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
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 کاملIrreducible Symmetric Group Characters of Rectangular Shape
where χ(1) denotes the dimension of the character χ and (n)k = n(n − 1) · · · (n − k + 1). Thus [8, (7.6)(ii)][12, p. 349] χ(1) is the number f of standard Young tableaux of shape λ. Identify λ with its diagram {(i, j) : 1 ≤ j ≤ λi}, and regard the points (i, j) ∈ λ as squares (forming the Young diagram of λ). We write diagrams in “English notation,” with the first coordinate increasing from to...
متن کاملDefect of characters of the symmetric group
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 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2021
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2021.107943