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Radicals of symmetric cellular algebras

Yanbo Li (2013)

Colloquium Mathematicae

For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.

rc-graphs and Schubert polynomials.

Bergeron, Nantel, Billey, Sara (1993)

Experimental Mathematics

Recognizing cluster algebras of finite type.

Seven, Ahmet I. (2007)

The Electronic Journal of Combinatorics [electronic only]

Representations of the covering groups of the symmetric groups and their combinatorics.

Bessenrodt, Christine (1994)

Séminaire Lotharingien de Combinatoire [electronic only]

RSK bases and Kazhdan-Lusztig cells

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

Annales de l’institut Fourier

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.