Given any simple Lie superalgebra g, we investigate the structure of an arbitrary simple weight g-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuper-algebra. Then we classify the cuspidal Levi sub...

The structure and representations of the quantum general linear supergroup GLq(m|n) are studied systematically by investigating the Hopf superalgebra Gq of its representative functions. Gq is factorized into G π q G π̄ q , and a Peter Weyl basis is constructed for each factor. Parabolic induction for the quantum supergroup is developed. The underlying geometry of induced representations is discu...

Throughout this paper, G denotes a fixed, not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series [L9] which attempts to develop a theory of character sheaves on G. The numbering of the sections and references continues that of the earlier Parts. Section 23 is a generalization of results in [L3, II,§7]. It is a preparation for ...

The main purpose of this note is to prove that the quantum coordinate algebra A[U ] is free over the ring A = Z[v, v−1]. In [L1], Lusztig defined the quantum coordinate algebra over Q[v, v−1] and prove that it is free as Q[v, v−1]-module. In [APW], Andersen, Polo, and Wen defined the quantum coordinate algebra over the ring A(p,v−1) and proved that the coordinate algebra is free. The main idea ...

Given any simple Lie superalgebra g, we investigate the structure of an arbitrary simple weight g-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuper-algebra. Then we classify the cuspidal Levi sub...

The quantum supergroup OSPq(1u2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter–Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes’ theory. Parabolic induction is developed by employing the quantum homogeneous supervector ...

The irreducible unitary representations of GL(n, ~) have been classified by D. Vogan in [V2]. In his work, four families of representations play a special role. They are (i) the one dimensional unitary representations and (ii) their complementary series; (iii) Speh's representations and (iv) their complementary series. These representations serve as "building blocks" in the sense that every irr...

In the present work the effect of Cu-Water nanofluid, as heat transfer fluid, on the performance of a parabolic solar collector was studied numerically. The temperature field, thermal efficiency, mean-outlet temperatures have been evaluated and compared for the conventional parabolic collectors and nanofluid based collectors. Further, the effect of various parameters such as fluid velocity, vol...

In the present work the effect of Cu-Water nanofluid, as heat transfer fluid, on the performance of a parabolic solar collector was studied numerically. The temperature field, thermal efficiency, mean-outlet temperatures have been evaluated and compared for the conventional parabolic collectors and nanofluid based collectors. Further, the effect of various parameters such as fluid velocity, vol...

in this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎in particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.