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Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

We construct a subalgebra Σ ′ ( W n ) of dimension 2 · 3 n - 1 of the group algebra of the Weyl group W n of type B n containing its usual Solomon algebra and the one of 𝔖 n : Σ ′ ( W n ) is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras Σ ′ ( W n ) → Z Irr ( W n ) . Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to W n . In an appendix, P. Baumann and C. Hohlweg present in an explicit and...

Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra

Joachim Seifert (1997)

Banach Center Publications

Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.

Generalized Induction of Kazhdan-Lusztig cells

Jérémie Guilhot (2009)

Annales de l’institut Fourier

Following Lusztig, we consider a Coxeter group W together with a weight function. Geck showed that the Kazhdan-Lusztig cells of W are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of W which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of W are cells in the whole group, and we decompose the affine Weyl group of type G into left...

Generalized symmetry classes of tensors

Gholamreza Rafatneshan, Yousef Zamani (2020)

Czechoslovak Mathematical Journal

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.

Generic representations of orthogonal groups: projective functors in the category ℱ q u a d

Christine Vespa (2008)

Fundamenta Mathematicae

We continue the study of the category of functors ℱ q u a d , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in ℱ q u a d ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in ℱ q u a d : P H ₀ and P H ₁ . As an application of these two decompositions, we give a complete description of the polynomial functors...

Graded blocks of group algebras with dihedral defect groups

Dusko Bogdanic (2011)

Colloquium Mathematicae

We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.

Currently displaying 281 – 300 of 995