The centers of spin symmetric group algebras and Catalan numbers
نویسندگان
چکیده
منابع مشابه
Double Affine Hecke Algebras for the Spin Symmetric Group
We introduce a new class (in two versions, Au and Bu) of rational double affine Hecke algebras (DaHa) associated to the spin symmetric group. We establish the basic properties of the algebras, such as PBW and Dunkl representation, and connections to Nazarov’s degenerate affine Hecke algebra and to a new degenerate affine Hecke algebra introduced here. We formulate a precise connection between t...
متن کاملCuntz-krieger Algebras and a Generalization of Catalan Numbers
We first observe that the relations of the canonical generating isometries of the Cuntz algebra ON are naturally related to the N-colored Catalan numbers. For a directed graph G, we generalize the Catalan numbers by using the canonical generating partial isometries of the Cuntz-Krieger algebra O AG for the transition matrix A of G. The generalized Catalan numbers cGn , n = 0, 1, 2, . . . enumer...
متن کاملCanonical Characters on Quasi-Symmetric Functions and Bivariate Catalan Numbers
Every character on a graded connected Hopf algebra decomposes uniquely as a product of an even character and an odd character [2]. We obtain explicit formulas for the even and odd parts of the universal character on the Hopf algebra of quasi-symmetric functions. They can be described in terms of Legendre’s beta function evaluated at halfintegers, or in terms of bivariate Catalan numbers: C(m, n...
متن کاملHecke Algebras and Schur Algebras of the Symmetric Group
These notes give a fully self{contained introduction to the (modular) representation theory of the Iwahori{Hecke algebras and the q{Schur algebras of the symmetric groups. The central aim of this work is to give a concise, but complete, and an elegant, yet quick, treatment of the classiication of the simple modules and of the blocks of these two important classes of algebras. Our approach is co...
متن کاملCoincidences of Catalan and Q-catalan Numbers
Let Cn and Cn(q) be the nth Catalan number and the nth q-Catalan number, respectively. In this paper, we show that the Diophantine equation Cn = Cm(q) has only finitely many integer solutions (m,n, q) with m > 1, n > 1, q > 1. Moreover, they are all effectively computable. – To Professor Carl Pomerance on his 65th birthday
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2008
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-008-0128-1