The representation theory of Hecke algebras has been an important part toward understanding (ordinary or modular) representation theories of finite groups of Lie type. Schur algebras, as endomorphism algebras, connects the representation theory of general linear groups and the representations of symmetric groups via Schur-Weyl duality. The quantum version of Schur-Weyl duality is established by...

We propose a Lagrangian density for M-Theory which is purely topological using Gelfand-Fuchs cohomology which characterises up to homotopy Γq-structures and hence foliations in particular. Then, using a physical principle and S-duality, we conjecture on the existence of certain plane fields on S. PACS classification: 11.10.-z; 11.15.-q; 11.30.-Ly

Every finite, self-dual, regular (or chiral) 4-polytope of type {3, q, 3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edgebut not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.

When we were at the beginnings of our careers Sergei’s support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman-Murakami-Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity...

We show that the coefficients of Ramanujan’s mock theta function f(q) are the first non-trivial coefficients of a canonical sequence of modular forms. This fact follows from a duality which equates coefficients of the holomorphic projections of certain weight 1/2 Maass forms with coefficients of certain weight 3/2 modular forms. This work depends on the theory of Poincaré series, and a modifica...

If a nonsymmetric P-polynomial association scheme, or equivalently. a distanceregular digraph, has diameter d and girth g. then d = g or d = g 1, by Damerell’s theorem. The dual of this theorem was proved by Leonard. In this paper, we prove that the diameter of a nonsymmetric Pand Q-polynomial association scheme is one less than its girth and its cogirth. We also give a structure theorem for a ...

We examine a dual theory of a Supersymmetric Standard Model(SSM) in terms of an SU(3)C gauge group. In this scenario, it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the weak scale. Moreover, the supersymmetric Higgs mass parameter μ can naturally be expected to be small. This model automatically induces nine pairs of composite ...

We present a dual description for SU (N) supersymmetric gauge theory with an anti-symmetric tensor and fundamentals, and no superpotential. This duality is derived from the dualities of Seiberg. Under a perturbation of the superpotential, the dual theory breaks supersymmetry at tree level. 10/95 One year ago, a remarkable feature of gauge field theories was discovered [1]. Certain N =1 supersym...

We show how, by making use of a new basis of the IIB supergravity axion-dilaton coset, SL(2,R)/SO(2), 7-branes that belong to different conjugacy classes of the duality group SL(2,R) naturally couple to IIB supergravity with appropriate source terms characterized by an SL(2,R) charge matrix Q. The conjugacy classes are determined by the value of the determinant of Q. The (p, q) 7-branes are the...

Connections between set-theoretic Yang-Baxter and reflection equations quantum integrable systems are investigated. We show that $R$-matrices expressed as twists of known solutions. then focus on twisted algebras we derive the associated defining algebra relations for being Baxterized solutions $A$-type Hecke ${\cal H}_N(q=1)$. in case there exists a ``boundary'' finite sub-algebra some special...