scholarly journals On the restriction of irreducible characters of symmetric groups to Sylow p -subgroups

2017 ◽  
Vol 483 ◽  
pp. 37-57 ◽  
Author(s):  
Eugenio Giannelli
Keyword(s):  
Symmetric Groups ◽  
Irreducible Characters

Orthogonal $*$-basis of relative symmetry classes of polynomials

2015 ◽  
Vol 30 ◽  
Author(s):  
Kijti Rodtes
Keyword(s):  
Finite Groups ◽  
Symmetric Groups ◽  
Orthogonal Basis ◽  
Irreducible Characters ◽  
Symmetry Classes

In this note, the existence of orthogonal ∗-basis of the symmetry classes of polynomials is discussed. Analogously to the orthogonal ∗-basis of symmetry classes of tensor, some criteria for the existence of the basis for finite groups are provided. A condition for the existence of such basis of symmetry classes of polynomials associated to symmetric groups and some irreducible characters is also investigated.

scholarly journals Character correspondences for symmetric groups and wreath products

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Anton Evseev
Keyword(s):  
Finite Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Irreducible Characters ◽  
Arbitrary Finite Group

AbstractThe Alperin–McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its

scholarly journals Young–Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants

2020 ◽  
pp. 2150123
Author(s):  
A. Brini ◽  
A. Teolis
Keyword(s):  
Polynomial Algebra ◽  
Symmetric Groups ◽  
Lie Superalgebras ◽  
General Linear ◽  
Linear Combinations ◽  
Irreducible Characters ◽  
New Class ◽  
Linear Generators ◽  
Capelli Identities ◽  
Quantum Immanants

The set of standard Capelli bitableaux and the set of standard Young–Capelli bitableaux are bases of [Formula: see text], whose action on the Gordan–Capelli basis of polynomial algebra [Formula: see text] have remarkable properties (see, e.g. [A. Brini, A. Palareti and A. Teolis, Gordan–Capelli series in superalgebras, Proc. Natl. Acad. Sci. USA 85 (1988) 1330–1333; A. Brini and A. Teolis, Young–Capelli symmetrizers in superalgebras, Proc. Natl. Acad. Sci. USA 86 (1989) 775–778; A. Brini and A. Teolis, Capelli bitableaux and [Formula: see text]-forms of general linear Lie superalgebras, Proc. Natl. Acad. Sci. USA 87 (1990) 56–60; A. Brini and A. Teolis, Capelli’s theory, Koszul maps, and superalgebras, Proc. Natl. Acad. Sci. USA  90 (1993) 10245–10249.]). We introduce a new class of elements of [Formula: see text], called the Capelli immanants, that can be efficiently computed and provide a system of linear generators of [Formula: see text]. The Okounkov quantum immanants [A. Okounkov, Quantum immanants and higher Capelli identities, Transform Groups 1 (1996) 99–126; A. Okounkov, Young basis, Wick formula, and higher Capelli identities, Int. Math. Res. Not. 1996(17) (1996) 817–839.] — quantum immanants, for short — are proved to be simple linear combinations of diagonal Capelli immanants, with explicit coefficients. Quantum immanants can also be expressed as sums of double Young–Capelli bitableaux. Since double Young–Capelli bitableaux uniquely expands into linear combinations of standard Young–Capelli bitableaux, this leads to canonical presentations of quantum immanants, and, furthermore, it does not involve the computation of the irreducible characters of symmetric groups.

scholarly journals On Multiple Transitivity of Permutation Groups

1961 ◽  
Vol 18 ◽  
pp. 93-109 ◽  
Author(s):  
Tosiro Tsuzuku
Keyword(s):  
Symmetric Group ◽  
Permutation Group ◽  
Irreducible Character ◽  
Symmetric Groups ◽  
Transitive Group ◽  
Permutation Groups ◽  
Irreducible Characters ◽  
Interesting Theorem

It is well known that a doubly transitive group has an irreducible character χ1 such that χ1(R) = α(R) − 1 for any element R of and a quadruply transitive group has irreducible characters χ3 and χ3 such that χ2(R) = where α(R) and β(R) are respectively the numbers of one cycles and two cycles contained in R. G. Frobenius was led to this fact in the connection with characters of the symmetric groups and he proved the following interesting theorem: if a permutation group of degree n is t-ply transitive, then any irreducible character of the symmetric group of degree n with dimension at most equal to is an irreducible character of .

scholarly journals Schur $q$-functions and Spin Characters of Symmetric Groups I

10.37236/1278 ◽  
1995 ◽  
Vol 3 (2) ◽  
Author(s):  
Alun Morris ◽  
A. A. Abdel-Aziz
Keyword(s):  
Symmetric Groups ◽  
Schur Functions ◽  
Irreducible Characters ◽  
Spin Characters

Inspired by the early work of D.E.Littlewood and A.R.Richardson, Schur functions have been used to give useful combinatorial formulae for determining explicit values for the irreducible characters of the symmetric groups.In this,the first of two papers,we consider how Schur Q-functions can be used to obtain combinatorial formulae for the irreducible spin (projective) characters of symmetric groups.

scholarly journals Limits of Characters of Wreath Products 𝔖n(T) of a Compact Group T With the Symmetric Groups and Characters of 𝔖∞(T), I

2009 ◽  
Vol 193 ◽  
pp. 1-93
Author(s):  
Takeshi Hirai ◽  
Etsuko Hirai ◽  
Akihito Hora
Keyword(s):  
Compact Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Continuous Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Irreducible Characters ◽  
Induced Representations ◽  
Irreducible Components ◽  
Necessary And Sufficient

AbstractIn the first half of this paper, all the limits of irreducible characters of Gn = 𝔖n(T) as n → ∞ are calculated. The set of all continuous limit functions on G = 𝔖 ∞(T) is exactly equal to the set of all characters of G determined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters of Gn to have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations of Gn which are usually reducible. The limits turn out to be characters of G, and we analyse which of irreducible components are responsible to these limits.

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