Structure and representations on the quantum supergroup OSPq(2|2n)

Abstract

Master function approach to quantum solvable models on SL (2,c) and SL (2,c)/ GL (1,c) manifolds J. Math. Phys. 41, 505 (2000) The structure and representations of the quantum supergroup OSP q (2͉2n) are studied systematically. The algebra of functions on the quantum supergroup, which specifies the quantum supergroup itself, is taken to be the superalgebra generated by the matrix elements of the vector representation of the quantized universal superalgebra U q (osp(2͉2n)). It is shown that the algebra of functions is dense in the full dual U q (osp(2͉2n))* of U q (osp(2͉2n)) and possesses a Hopf superalgebra structure. The left integral and right integral on the quantum supergroup are discussed. Induced representations are developed using the noncommutative geometry of quantum homogeneous supervector bundles, and a geometric realization of irreducible representations is obtained.

Invariant integration on classical and quantum Lie supergroups

“…We will take the algebra A of functions on OSP q (2|2n) to be the subalgebra of U q (g) • generated by the elements t ab . In [26] we have shown:…”