The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group

Fabio Scarabotti

Displaying similar documents to “The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group”

Character formula for wreath products of compact groups with the infinite symmetric group

Takeshi Hirai, Etsuko Hirai (2006)

Banach Center Publications

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Let $G =_{\infty} (T)$ be the wreath product of a compact group T with the infinite symmetric group $_{\infty}$ . We study the characters of factor representations of finite type of G, and give a formula which expresses all the characters explicitly.

On symmetric functions and the spin characters of $S_{n}$

John R. Stembridge (1990)

Banach Center Publications

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Two examples of subspaces in $L^{2 l}$ spanned by characters of finite order

Mats Erik Andersson (2001)

Colloquium Mathematicae

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By a Fourier multiplier technique on Cantor-like Abelian groups with characters of finite order, the norms from L² into $L^{2 l}$ of certain embeddings of character sums are computed. It turns out that the orders of the characters are immaterial as soon as they are at least four.

Finite $p$ -groups with exactly two nonlinear non-faithful irreducible characters

Yali Li, Xiaoyou Chen, Huimin Li (2019)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group with exactly two nonlinear non-faithful irreducible characters. We discuss the properties of $G$ and classify finite $p$ -groups with exactly two nonlinear non-faithful irreducible characters.

Finite groups with two rows which differ in only one entry in character tables

Wenyang Wang, Ni Du (2021)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. If $G$ has two rows which differ in only one entry in the character table, we call $G$ an RD1-group. We investigate the character tables of RD1-groups and get some necessary and sufficient conditions about RD1-groups.

Scalar differential concomitants of first order of a symmetric connexion $Γ_{j k}^{i}$ in the two-dimensional space and their applications

Michał Lorens (1980)

Annales Polonici Mathematici

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Symmetry classes of tensors associated with the semi-dihedral groups $S D_{8 n}$

Mahdi Hormozi, Kijti Rodtes (2013)

Colloquium Mathematicae

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We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups $S D_{8 n}$ . In particular, a necessary and sufficient condition for the existence of such a basis associated with $S D_{8 n}$ and degree two characters is given.

Recognition of characteristically simple group $A_{5} \times A_{5}$ by character degree graph and order

Maryam Khademi, Behrooz Khosravi (2018)

Czechoslovak Mathematical Journal

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The character degree graph of a finite group $G$ is the graph whose vertices are the prime divisors of the irreducible character degrees of $G$ and two vertices $p$ and $q$ are joined by an edge if $p q$ divides some irreducible character degree of $G$ . It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically...

Congruences modulo $ℓ$ between $ϵ$ factors for cuspidal representations of $G L (2)$

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

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Let $ℓ \neq p$ be two different prime numbers, let $F$ be a local non archimedean field of residual characteristic $p$ , and let ${\bar{𝐐}}_{ℓ}, {\bar{𝐙}}_{ℓ}, {\bar{𝐅}}_{ℓ}$ be an algebraic closure of the field of $ℓ$ -adic numbers $𝐐_{ℓ}$ , the ring of integers of ${\bar{𝐐}}_{ℓ}$ , the residual field of ${\bar{𝐙}}_{ℓ}$ . We proved the existence and the unicity of a Langlands local correspondence over ${\bar{𝐅}}_{ℓ}$ for all $n \geq 2$ , compatible with the reduction modulo $ℓ$ in [V5], without using $L$ and $ϵ$ factors of pairs. We conjecture that the Langlands local correspondence over ${\bar{𝐐}}_{ℓ}$ respects congruences...

A class of irreducible polynomials

Joshua Harrington, Lenny Jones (2013)

Colloquium Mathematicae

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Let $f (x) = x ⁿ + k_{n - 1} x^{n - 1} + k_{n - 2} x^{n - 2} + \dots + k ₁ x + k ₀ \in ℤ [x]$ , where $3 \leq k_{n - 1} \leq k_{n - 2} \leq \dots \leq k ₁ \leq k ₀ \leq 2 k_{n - 1} - 3$ . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2 k_{n - 1} - 3$ on the coefficients of f(x) is the best possible in this situation.

The mean value of |L(k,χ)|² at positive rational integers k ≥ 1

Stéphane Louboutin (2001)

Colloquium Mathematicae

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Let k ≥ 1 denote any positive rational integer. We give formulae for the sums $S_{o d d} (k, f) = \sum_{χ (- 1) = - 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 odd Dirichlet characters modulo f > 2) whenever k ≥ 1 is odd, and for the sums $S_{e v e n} (k, f) = \sum_{χ (- 1) = + 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 even Dirichlet characters modulo f>2) whenever k ≥ 1 is even.

Some properties of certain subclasses of bounded Mocanu variation with respect to $2 k$ -symmetric conjugate points

Rasoul Aghalary, Jafar Kazemzadeh (2019)

Mathematica Bohemica

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We introduce subclasses of analytic functions of bounded radius rotation, bounded boundary rotation and bounded Mocanu variation with respect to $2 k$ -symmetric conjugate points and study some of its basic properties.

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

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The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....

Representations of $S_{n}$ and $G L_{n}$ and the q-Schur algebra

Gordon James (1990)

Banach Center Publications

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On a certain generalization of spherical twists

Yukinobu Toda (2007)

Bulletin de la Société Mathématique de France

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This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of $(0, - 2)$ -curves on threefolds, or deforming $ℙ$ -objects introduced by D.Huybrechts and R.Thomas.

Quiver varieties and the character ring of general linear groups over finite fields

Emmanuel Letellier (2013)

Journal of the European Mathematical Society

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Given a tuple $(𝒳_{1}, ..., 𝒳_{k})$ of irreducible characters of $G L_{n} (F_{q})$ we define a star-shaped quiver $Γ$ together with a dimension vector $v$ . Assume that $(𝒳_{1}, ..., 𝒳_{k})$ is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product $𝒳_{1} \otimes \dots \otimes 𝒳_{k}$ as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to $(Γ, v)$ . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied,...

A cluster algebra approach to $q$ -characters of Kirillov–Reshetikhin modules

David Hernandez, Bernard Leclerc (2016)

Journal of the European Mathematical Society

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We describe a cluster algebra algorithm for calculating $q$ -characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra $U_{q} (\hat{𝔤})$ . This yields a geometric $q$ -character formula for tensor products of Kirillov–Reshetikhin modules. When $𝔤$ is of type $A, D, E$ , this formula extends Nakajima’s formula for $q$ -characters of standard modules in terms of homology of graded quiver varieties.

$H^{p}$ spaces on bounded symmetric domains

Kyong T. Hahn, Josephine Mitchell (1973)

Annales Polonici Mathematici

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Group Structures and Rectifiability in Powers of Spaces

G. J. Ridderbos (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that if some power of a space X is rectifiable, then $X^{π w (X)}$ is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangel’skiĭ. We also show that in Mal’tsev spaces of point-countable type, character and π-character coincide.

A new approach to Hom-left-symmetric bialgebras

Qinxiu Sun, Qiong Lou, Hongliang Li (2021)

Czechoslovak Mathematical Journal

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The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that $s$ -matrix is a solution of the Hom- $S$ -equation by a cocycle condition.

Generalized symmetry classes of tensors

Gholamreza Rafatneshan, Yousef Zamani (2020)

Czechoslovak Mathematical Journal

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Let $V$ be a unitary space. For an arbitrary subgroup $G$ of the full symmetric group $S_{m}$ and an arbitrary irreducible unitary representation $Λ$ of $G$ , we study the generalized symmetry class of tensors over $V$ associated with $G$ and $Λ$ . Some important properties of this vector space are investigated.

An inequality for spherical Cauchy dual tuples

Sameer Chavan (2013)

Colloquium Mathematicae

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Let T be a spherical 2-expansive m-tuple and let $T^{}$ denote its spherical Cauchy dual. If $T^{}$ is commuting then the inequality $\binom{\sum_{| β | = k} {(β!)}^{- 1} {(T^{})}^{β} (T^{}) *^{β} \leq (k + m - 1}{k) \sum_{| β | = k} {(β!)}^{- 1} (T^{}) *^{β} {(T^{})}^{β}}$ holds for every positive integer k. In case m = 1, this reveals the rather curious fact that all positive integral powers of the Cauchy dual of a 2-expansive (or concave) operator are hyponormal.

On sharp characters of type ${- 1, 0, 2}$

Alireza Abdollahi, Javad Bagherian, Mahdi Ebrahimi, Maryam Khatami, Zahra Shahbazi, Reza Sobhani (2022)

Czechoslovak Mathematical Journal

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For a complex character $χ$ of a finite group $G$ , it is known that the product $sh (χ) = \prod_{l \in L (χ)} (χ (1) - l)$ is a multiple of $| G |$ , where $L (χ)$ is the image of $χ$ on $G - {1}$ . The character $χ$ is said to be a sharp character of type $L$ if $L = L (χ)$ and $sh (χ) = | G |$ . If the principal character of $G$ is not an irreducible constituent of $χ$ , then the character $χ$ is called normalized. It is proposed as a problem by P. J. Cameron and M. Kiyota, to find finite groups $G$ with normalized sharp characters of type ${- 1, 0, 2}$ . Here we prove that such a group with nontrivial...

Results related to Huppert’s $ρ$ - $σ$ conjecture

Xia Xu, Yong Yang (2023)

Czechoslovak Mathematical Journal

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We improve a few results related to Huppert’s $ρ$ - $σ$ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.