Download e-book for kindle: Quantum group symmetry and q-tensor algebras by L. C. Biedenharn

By L. C. Biedenharn

ISBN-10: 9810223315

ISBN-13: 9789810223311

This quantity encompasses a selection of study articles through best specialists in crew thought, and stories of numerous obtainable surveys of contemporary learn within the quarter. The compilation supply an outline of the range of subject matters and purposes that curiosity latest workforce theorists. the themes lined during this quantity comprise: personality concept, combinatorial workforce concept, kinds of teams, conjugacy periods, profinite teams, graphs attached with teams, subgroup constitution, illustration idea

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And a] for i = 1 , . . 25. 28 1. 26) becomes exactly the algebra of boson operators, the Heisenberg-Weyl algebra f)4. 2. We may assume that a' is the Hermitian conjugate of a' and that AF» is Hermitian, that is, the g-boson algebra admits an involutive anti-automorphism, so that we may impose (<*')* = a*, (•&)* = a\ (jVjtmJV*. This leads to a suitable inner product, considered below, but only for q 6 K + ; at roots of unity we impose more general Hermiticity relations. 3. The g-boson algebra is invariant under the U(l) transformation a" - .

Are non-negative integers, A; are the principal minors of the matrix C§, and (s is t i e right component of {g in its decomposition into lower and upper triangular matrices (see [98, Chapter VII]). i-u -^ . f 3 i2,„i-i; where the antisymmetric combination * , , ^ . is the minor of the nx n matrix (* ), where 2 are the homogeneous coordinates. This is discussed by Lohe and Hurst [99] to which we refer for further details. However, we develop here the generalization to quantum groups only for W,(su(2}).

N ) with all other commutators zero. 22 The map (the "Jordan map") J : Ea -» Xa preserves all commutators: J{[Ea, E0]) = [J(Ea), J(Ep)], that is, the Jordan map is a Lie algebra hhmomorphism. 5 Representations of Unitary Quantum Groups 25 This construction, transforming the fundamental, defining, matrix representation of the generators of a Lie group into a generic operator realization, essentially solves, at one stroke, the problem of constructing all unitary irreps and (with a bit more work) all tensor operator matrix elements of all compact Lie groups!

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Quantum group symmetry and q-tensor algebras by L. C. Biedenharn

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