# The 0-Rook, and 0-Renner Monoids

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Time: 11:00 -- Location: Salle Philippe Flajolet du LIX

We show that a proper degeneracy at $$q = 0$$ of the $$q$$-deformed rook monoid of Solomon is the algebra of a monoid $$R_n^0$$ namely the 0-rook monoid, in the same vein as Norton's 0-Hecke algebra being the algebra of a monoid $$H_n^0 := H_n^0(A)$$ (in Cartan type A). As expected, $$R_n^0$$ is closely related to the latter: it contains the $$H_n^0(A)$$ monoid and is a quotient of $$H_n^0(B)$$. This talk will be about the way to define it, using actions on permutations and rook vectors, with some algorithms.

Finally, the rook monoid is a particular case of a family of monoids indexed by the Weyl groups, called the Renner monoids. We show that we can also define a "0-Renner monoid", and use this to give a proper characterization of elements of renner monoids.

Category: seminars
Tags: Combi seminar combinatorics