Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...

Let G be the group with Borel subgroup B, associated to a Kac-Moody Lie algebra [unk] (with Weyl group W and Cartan subalgebra [unk]). Then H(*)(G/B) has, among others, four distinguished structures (i) an algebra structure, (ii) a distinguished basis, given by the Schubert cells, (iii) a module for W, and (iv) a module for Hecke-type operators A(w), for w [unk] W. We construct a ring R, which ...

In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...

This paper reports the design of a sophisticated wysiwyg L a T E X-like typesetting system Vi e w T E X. Our approach is based on the Model-View-Controller (MVC) user-interface paradigm, as originated from the Smalltalk community. According to the paradigm, the Vi e w T E X system is decomposed into the sub-editor (model) module, the redisplay (view) module, and the user-commands (controller) m...

In a previous study [Li3], the physical super selection principle in vertex operator algebra theory seems to tell us that for a vertex operator algebra V , one should be able to obtain each irreducible V -module from the adjoint module V by changing certain things. To a certain extent, what we are expecting is an analogue of the orbital construction of representations for a Lie group [Ki]. This...

(5.1) Flat deformations: Let K/Qp be a finite extension with residue field k. Let W = W (k) and K0 = FrW. We consider a finite dimensional F-vector space equipped with a continuous action of GK . Fix an algebraic closure K̄ of K, and let GK = Gal(K̄/K). Recall that a representation of GK on a finite abelian p-group is called flat if it arises from a finite flat group scheme over OK . The followin...

We give a new Banach module characterization of W *-modules, also known as selfdual Hilbert C *-modules over a von Neumann algebra. This leads to a generalization of the notion, and the theory, of W *-modules, to the setting where the operator algebras are σ-weakly closed algebras of operators on a Hilbert space. That is, we find the appropriate weak* topology variant of our earlier notion of r...

Abstract In this paper, a concentrating photovoltaic system (CPV) by using compound parabolic concentrator and monocrystalline solar module has been designed studied theoretically under concentration ratio of 3.16x. The performance the is over course day from 8:00 AM to 16:00 PM for 12 months Iraq-Baghdad conditions. Current in short circuit (I sc ), voltage an open (V oc ) as well maximum powe...

A rectangular-waveguide output UTC-PD module integrating a HEMT power amplifier has been developed for operation in the 125-GHz band. The fabricated module exhibits maximum output power of more than 14 dBm with nearly flat frequency dependence in the 115-135GHz range. A 10-Gbit/s error-free wireless transmission at 125GHz with a minimum sensitivity of −34 dBm for a bit-error-rate of 10−12 is al...