RSK bases and Kazhdan-Lusztig cells

K. N. Raghavan; Preena Samuel; K. V. Subrahmanyam

Displaying similar documents to “RSK bases and Kazhdan-Lusztig cells”

Diamond representations of $𝔰𝔩 (n)$

Didier Arnal, Nadia Bel Baraka, Norman J. Wildberger (2006)

Annales mathématiques Blaise Pascal

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In [6], there is a graphic description of any irreducible, finite dimensional $𝔰𝔩 (3)$ module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional $𝒰_{q} (𝔰𝔩 (3))$ -modules. In the present work, we generalize this construction to $𝔰𝔩 (n)$ . We show it is in fact a description of the reduced shape algebra, a quotient of the shape algebra of $𝔰𝔩 (n)$ . The basis used in [

Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

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Let $Λ$ be a preprojective algebra of type $A, D, E$ , and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $Sub Q$ for $Q$ an injective $Λ$ -module, and we introduce a mutation operation between complete rigid modules in $Sub Q$ . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$ .

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé, Christophe Hohlweg (2006)

Annales de l’institut Fourier

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We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ 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 $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . 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...