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Displaying similar documents to “Tableaux in the Whitney module of a matroid.”

RSK bases and Kazhdan-Lusztig cells

K. N. Raghavan, Preena Samuel, K. V. Subrahmanyam (2012)

Annales de l’institut Fourier

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From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, “ RSK bases” are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory, both ordinary and modular, of the symmetric group are discussed.

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 [

Submodule of free Z-module

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

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In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their...

Z-modules

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].