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Unitary quasifinite representations of W_{\infty}
(Springer, 2000-01)
We classify the unitary quasi-finite highest-weight modules over the Lie algebra W and realize them in terms of unitary highest-weight representations of the Lie algebra of infinite matrices with finitely many nonzero diagonals.
Kleiner's theorem for unitary representations of posets
(ELSEVIER SCIENCE INCNEW YORK, 2013-08-02)
A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued ...
Casimir operators of complementary unitary groups
(1974-01-01)
A relationship between all the generalized Casimir operators of complementary unitary groups is derived, both in the fermion and boson realizations of the corresponding Lie algebras. It is shown that the number of independent ...
Unitary representations of affine hecke algebras related to macdonald spherical functions
(ACADEMIC PRESS, 2012)
Unitary representations of affine hecke algebras related to macdonald spherical functions
(ACADEMIC PRESS, 2012)
Local unitary representations of the braid group and their applications to quantum computing
(Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas, 2016-07-01)
We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones ...
Unitary representations of affine Hecke algebras related to Macdonald spherical functions
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2012)
For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions ...
Unitary representations of cyclotomic rational Cherednik algebras
(2018)
We classify the irreducible unitary modules in category O-c for the rational Cherednik algebras of type G(r, 1, n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial ...