Incompressible representations of the Birman-Wenzl-Murakami algebra
نویسنده
چکیده
We construct a representation of the Birman-Wenzl-Murakami algebra acting on a space of polynomials in n variables vanishing when three points coincide. These polynomials are closely related to the Pfaffian state of the Quantum Hall Effect and to the components the transfer matrix eigenvector of a O(n) crossing loop model.
منابع مشابه
Symmetrizer and Antisymmetrizer of the Birman–wenzl–murakami Algebras
The Birman–Wenzl–Murakami algebra was first defined and independently studied by Birman andWenzl [1] and Murakami [4]. The Iwahori–Hecke algebras of Type A and the Birman–Wenzl–Murakami algebras naturally arise as centralizer algebras of tensor product corepresentations of quantum groups of Type A and of Type B, C, and D, respectively [5, 6]. Irreducible characters and primitive idempotents of ...
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Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertexand IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour generalization of the Birman-Wenzl-Murakami algebra can be constructed, which in turn are used to derive trigonometric solutions to the YangBaxter equation. In spirit, ...
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The affine Birman–Wenzl–Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
متن کامل“Dilute” Birman–Wenzl–Murakami Algebra
Explicit expressions for three series of R matrices which are related to a “dilute” generalisation of the Birman–Wenzl–Murakami algebra are presented. Of those, one series is equivalent to the quantum R matrices of the D (2) n+1 generalised Toda systems whereas the remaining two series appear to be new. A “dilute” generalisation of the Birman–Wenzl–Murakami (BWM) algebra [1, 2] has recently bee...
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تاریخ انتشار 2005