156 research outputs found
Generalized adjoint actions
The aim of this paper is to generalize the classical formula
by replacing
with any formal power series . We
also obtain combinatorial applications to -exponentials, -binomials, and
Hall-Littlewood polynomials.Comment: 5 pages, LaTeX, typos corrected, to appear in Journal of Lie Theor
Algebras of Quasi-Pl\"ucker Coordinates are Koszul
Motivated by the theory of quasi-determinants, we study non-commutative
algebras of quasi-Pl\"ucker coordinates. We prove that these algebras provide
new examples of non-homogeneous quadratic Koszul algebras by showing that their
quadratic duals have quadratic Gr\"obner bases.Comment: 15 pages, AMS tex, tikz figures. V2: small corrections based on
referee report. V3: Further minor changes. To appear in J. Pure Appl. Algebr
Noncommutative Catalan numbers
The goal of this paper is to introduce and study noncommutative Catalan
numbers which belong to the free Laurent polynomial algebra in
generators. Our noncommutative numbers admit interesting (commutative and
noncommutative) specializations, one of them related to Garsia-Haiman
-versions, another -- to solving noncommutative quadratic equations. We
also establish total positivity of the corresponding (noncommutative) Hankel
matrices and introduce accompanying noncommutative binomial coefficients.Comment: 12 pages AM LaTex, a picture and proof of Lemma 3.6 are added,
misprints correcte
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