graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

We use the conjectured strong-weak coupling worldsheet duality between the SL(2)/U (1) and Sine-Liouville conformal field theories to study some properties of degenerate operators and to compute correlation functions in CFT on AdS 3. The same quantities have been computed in the past by other means. The agreement between the different approaches provides new evidence for the duality. We also di...

Two families of q-Schur algebras associated to Hecke algebras of type D are introduced, and related to a family used by Geck, Gruber and Hiss [10], [11]. We prove that the algebras in one family, called the q-Schur algebras, are integrally free, stable under base change, and are standardly stratified if the base field has odd characteristic. In the so-called linear prime case of [10],[11], all ...

Let G be a classical algebraic group, X a maximal rank reductive subgroup and P a parabolic subgroup. This paper classifies when X\G/P is finite. Finiteness is proven using geometric arguments about the action of X on subspaces of the natural module for G. Infiniteness is proven using a dimension criterion which involves root systems. 1 Statement of results Let G be a classical algebraic group ...

This note contains a report of a proof by computer that the Fibonacci group F (2, 9) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that the group generators have infinite order, which of course implies that the group itself is infinite. The Fibonnacci groups F (2, n), for integers n ≥ 2, are ...

Let W be the Weyl group of a connected reductive group over a finite field. It is a consequence of the Borel-Tits rational conjugacy theorem for maximal split tori that for certain reflection subgroups W1 of W (including all parabolic subgroups), the elements of minimal reflection length in any coset wW1 are all conjugate, provided w normalises W1. We prove a sharper and more general result of ...

These working notes summarize the different approaches we have explored in order to classify a corpus of tweets related to the 2015 Spanish General Election (COSET 2017 task from IberEval 2017). Two approaches were tested during the COSET 2017 evaluations: Neural Networks with Sentence Embeddings (based on TensorFlow) and N-gram Language Models (based on SRILM). Our results with these approache...

These are notes for a class on double affine Hecke algebras and Macdonald polynomials given in the Fall of 2007 at the University of Minnesota. Here we introduce the (single and double) affine braid groups and Hecke algebras. We are following chapters 3,4, and 5 of Macdonald’s book [Mac]. There is also an (optional) aside giving applications to the T -equivariant K-theory of flag varieties G/B....

We examine the picture of emergent gravity arising from a mass deformed matrix model. Due to the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent ...

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...