The Planar Rook Algebra and Pascal's Triangle
نویسندگان
چکیده
منابع مشابه
The rook partition algebra
The rook partition algebra RPk(x) is a semisimple algebra for all but a finite number of values of x ∈ C that arises from looking at what commutes with the action of the symmetric group Sn on U ⊗k, where U is the direct sum of the natural representation and the trivial representation of Sn. We give a combinatorial description of this algebra, construct its irreducible representations, and exhib...
متن کاملRepresentations of the Rook-Brauer Algebra
We study the representation theory of the rook-Brauer algebra RBk(x), which has a of Brauer diagrams that allow for the possibility of missing edges. The Brauer, Temperley-Lieb, Motzkin, rook monoid, and symmetric group algebras are subalgebras of RBk(x). We prove that RBk(n+1) is the centralizer of the orthogonal group On(C) on tensor space and that RBk(n+1) and On(C) are in Schur-Weyl duality...
متن کاملQuantum symmetries of face models and the double triangle algebra
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra. R. TRINCHERO 1
متن کاملSymmetries of faces models and the double triangle algebra
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra(DTA). R. TRINCHERO 1
متن کاملOn the Symmetric Enveloping Algebra of Planar Algebra Subfactors
We give a diagrammatic description of Popa’s symmetric enveloping algebras associated to planar algebra subfactors. As an application we construct a natural family of derivations on these factors, and compute a certain free entropy dimension type quantity. Introduction Inspired by Voiculescu’s [19] description of the large N limit of the distribution of families of independent random matrices, ...
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: L’Enseignement Mathématique
سال: 2009
ISSN: 0013-8584
DOI: 10.4171/lem/55-1-3