see for instance [29]. Notice that the exponent p or q could be larger than N+2 N−2 . Hence the usual Sobolev space H 0 (Ω)×H1 0 (Ω) is not suitable to handle the problem. To study the problem (1.2) under the condition (1.3), a key observation was done by Hulshof and Van de Vorst [16], De Figueiredo and Felmer [9]. In order to solve this problem, the main idea is to destroy the symmetry between...

The parabolic category O for affine glN at level −N−e admits a structure of categorical representation sl˜e with respect to some endofunctors E and F. This contains smaller A that categorifies the higher Fock space. We prove functors F in are Koszul dual Zuckerman functors. key point proof is show functor can be decomposed terms components −N−e−1. To this, we use following fact from [9]: an act...

The point of these notes is to redefine some of their concepts in terms of the L-group. I observe, however, that it is best and indeed essential for further applications that their results be formulated for reductive groups rather than just for simply-connected semi-simple groups. I use the notation of CIRRAG (On the classification of irreducible representations of real algebraic groups) modifi...

Corresponding author and person to whom reprint request should be addressed: Michael Tuttle, MD Endocrinology Service Department of Medicine Memorial Sloan‐Kettering Cancer Center Zuckerman Building, Room 59