for a parabolic subgroup P ⊂ G. In Part I [Na 2], when g is classical, we have proved that any two symplectic resolutions of Ō are connected by a sequence of Mukai flops of type A or of type D. In this paper (Part II), we shall improve and generalize all arguments in Part I so that the exceptional Lie algebras can be dealt with. We shall replace all arguments of [Na 2] which use flags, by those...

We study the ∆-filtered modules for the Auslander algebra of k[T ]/Tn ⋊C2 where C2 is the cyclic group of order two. The motivation for this is the bijection between parabolic orbits in the nilradical of a parabolic subgroup of SLn and certain ∆-filtered modules for the Auslander algebra of k[T ]/Tn as found by Hille and Röhrle and Brüstle et al., cf. [HR99] [BHRR99]. Under this bijection, the ...

We examine the theory of induced representations for non-connected reductive p-adic groups for which G/G is abelian. We first examine the structure of those representations of the form IndGP 0(σ), where P 0 is a parabolic subgroup of G and σ is a discrete series representation of the Levi component of P . Here we develop a theory of R–groups, extending the theory in the connected case. We then ...

We present a new method of calculating intertwining operators between principal series representations of semisimple Lie groups G. Working in the compact realization we nd the eigenvalues of the operators on the K-types, and give several examples. Among the advantages of our method is its applicability to bundle-valued cases. 0. Introduction Intertwining operators of various forms play an impor...

Let G be a p-adic connected reductive group with Lie algebra g. For a parabolic subgroup P ⊂ G and a finite-dimensional locally analytic representation V of a Levi subgroup of P, we study the induced locally analytic G-representation W = IndP (V ). Our result is the following criterion concerning the topological irreducibility of W : If the Verma module U(g) U(p) V ′ associated to the dual repr...

The notion of matroid has been generalized to Coxeter matroid by Gelfand and Serganova. To each pair (W, P) consisting of a finite irreducible Coxeter group W and parabolic subgroup P is associated a collection of objects called Coxeter matroids. The (ordinary) matroids are the special case where W is the symmetric group (the An case) and P is a maximal parabolic subgroup. This generalization o...

Given an Artin group $A$ and a parabolic subgroup $P$, we study if every two elements of $P$ that are conjugate in $A$, also $P$. We provide algorithm to solve this decision problem satisfies three properties conjectured be true for group. partially the has $FC$-type, totally it is isomorphic free product spherical groups. In particular, show latter case, element contained unique minimal (by in...

The theory of Whittaker functors for GLn is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([5]). We define Whittaker functors for GSp 4 and study their properties. These functors correspond to the maximal parabolic subgroup of GSp 4 , whose unipotent radical is not commutative. We also study similar functors cor...

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. • If H is a non-parabolic subgroup of a relatively hyperb...

In this paper we consider various problems involving the action of a reductive group G on an affine variety V . We prove some general rationality results about the G-orbits in V . In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of G for such general G-actions. We apply our general rationality results to answer a question of S...