For each r = (r1, r2, . . . , rN ) ∈ C N we construct a highest weight module Mr of the Lie algebra W1+∞. The highest weight vectors are specific tau-functions of the N -th Gelfand–Dickey hierarchy. We show that these modules are quasifinite and we give a complete description of the reducible ones together with a formula for the singular vectors. hep-th/9510211

The problem of equivariant rigidity is the Γ-homeomorphism classification of Γ-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of Γ. In other words, this is the classification of cocompact EfinΓ-manifolds. We use surgery theory, algebraic K-theory, and the Farrell–Jones Conjecture to give this classification for a family of groups which satis...

Psychological aspects of adjustment to amputation are varied and not addressed in the present treatment regime. There is no research evidence available of psychological intervention and outcome in Indian scenario. One hundred and seventy-three consecutive patients with limb amputations were randomly assigned to psychotherapeutic intervention module (PIM, study group) (n = 90) and treatment as u...

We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually Z group is isomorphic to the hyperoctahedral triangulation of Sn−1, providing a class of groups G for which the simplicial boundary of a G-cocompact cube complex depends only on G. We also use this result to show that the cocompactly cubulated crystallographic groups in dimension n...

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space Hn for every n ≤ 19 (resp. n ≤ 6). When n = 7 or 8, they may be taken to be nonarithmetic. Furthermore, for 2 ≤ n ≤ 19, with the possible exceptions n = 16 and 17, the number of essentially distinct Coxeter groups in Hn with noncompact fundamental domain of volume ≤ V gr...

The Jørgensen number of a rank-two non-elementary Kleinian group Γ is J(Γ) = inf{|trX − 4|+ |tr[X,Y ]− 2| : 〈X,Y 〉 = Γ}. Jørgensen’s Inequality guarantees J(Γ) ≥ 1, and Γ is a Jørgensen group if J(Γ) = 1. This paper shows that the only torsion-free Jørgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic Jørgensen groups, and establishes a characterization of coco...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...

 A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

Let M be a convex cocompact, acylindrical hyperbolic 3-manifold of infinite volume, and let M? denote the interior core M. In this paper we show that any geodesic plane in is either closed or dense. We also only countably many planes are closed. These first rigidity theorems for cocompact 3-manifolds volume depend on topology