✍ Scribed by Phùng Ho Hai
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For a Hecke operator R, one defines the matrix bialgebra E R , which is considered as function algebra on the quantum space of endomorphisms of the quantum space associated to R. One generalizes this notion, defining the function algebra M RS on the quantum space of homomorphisms of two quantum spaces associated to two Hecke operators R and S, respectively. M RS can be considered as a quantum analog (or a deformation) of the function algebra on the variety of matrices of a certain degree. We provide two realizations of M RS as a quotient algebra and as a subalgebra of a tensor algebra, whence we derive interesting information about M RS , for instance the Koszul property, a formula for computing the Poincaré series. On M RS coact the bialgebras E R and E S . We study the two-sided ideals in M RS , invariant with respect to these actions, in particular, the determinantal ideals. We prove analogies of the fundamental theorems of invariant theory for these quantum groups and quantum hom-spaces.
📜 SIMILAR VOLUMES
Our investigations of conformal invariance are based on the theory of analytic representations of the conformal group and its universal covering group. With its help the action of the conformal group on free massless fields, Greenberg fields, Wick products of these fields, and the Thirring fields is