REPRESENTATION THEORY OF (MODIFIED) REFLECTION EQUATION ALGEBRA OF GL(m|n) TYPE
نویسنده
چکیده
Let R : V ⊗2 → V ⊗2 be a Hecke type solution of the quantum Yang– Baxter equation (a Hecke symmetry). Then, the Hilbert–Poincaré series of the associated R-exterior algebra of the space V is the ratio of two polynomials of degrees m (numerator) and n (denominator). Under the assumption that R is skew-invertible, a rigid quasitensor category SW(V(m|n)) of vector spaces is defined, generated by the space V and its dual V ∗, and certain numerical characteristics of its objects are computed. Moreover, a braided bialgebra structure is introduced in the modified reflection equation algebra associated with R, and the objects of the category SW(V(m|n)) are equipped with an action of this algebra. In the case related to the quantum group Uq(sl(m)), the Poisson counterpart of the modified reflection equation algebra is considered and the semiclassical term of the pairing defined via the categorical (or quantum) trace is computed.
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