∗-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include q-Minkowski and q-Euclidean spaces as additive braided groups. The duality between the ∗-braided groups of vectors and covectors is proved and some first applications to braided geometry are made.

This experiment will extend measurements of inclusive nucleon resonance electropro-duction cross sections from hydrogen and deuterium targets throughout the resonance region (1 < W 2 < 4 GeV 2) to span the four-momentum transfer range 0.5 < Q 2 < 7.5 (GeV/c) 2. The cross sections will be used in conjunction with existing deep inelastic, resonance , and elastic data for precision experimental te...

We investigate the analogue of S-duality for 2-d gravity. Our analysis is based in a partition function associated to the Katanaev-Volovich type action for 2-d gravity. We find a S-dual 2-d gravitational action which is related to the original 2-d gravitational action by strong-weak duality transformation. PACS: 04.60.-m; 04.65.+e; 11.15.-q; 11.30.Ly July, 2001 ∗ [email protected]

classes in N(p,q). We show that X(p,q) with the quotient topology is homeomorphic to the compact, connected quotient space G(p, so(q,Â)) / SL(q,Â), where SL(q,Â) acts on so(q,Â) and the associated Grassmann manifold G(p, so(q,Â)) by g(Z) = gZgt for Z ∈ so(q,Â) and g ∈ SL(q,Â). It follows immediately that X(p,q) is homeomorphic to X(D−p,q), where D = dim so(q,Â) = (1/2)q(q−1) (duality). For each...

Abstract We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) functors give new interpretation representations the general linear groups GL n , (polynomial) symmetric pair ( $$ {U}_{Q,q}^B U Q , q ...

The twin group TWn on n strands is the generated by $t_{1}, \dots , t_{n-1}$ with defining relations ${t_{i}^{2}}=1$ titj = tjti if |i − j| > 1. We find a new instance of semisimple Schur–Weyl duality for tensor powers natural n-dimensional reflection representation TWn, depending parameter q. At q 1, coincides permutation symmetric group, so may be regarded as q-analogue one motivating definit...

It is shown that all the (p, q) dyon bound states exist and are unique in N = 4 and N = 2 with four massless flavours supersymmetric SU(2) Yang-Mills theories, where p and q are any relatively prime integers. The proof can be understood in the context of field theory alone, and does not rely on any duality assumption. We also give a general physical argument showing that these theories should h...

The duality and primitivity of the association scheme Qua(n, q) of quadratic forms in n variables and the association scheme Sym(n, q) of symmetric bilinear forms in n variables over the finite field Fq are discussed by Wang et al. [Association schemes of quadratic forms and symmetric bilinear forms, J. Algebraic Combin. 17 (2003) 149–161]. In this paper, eigenvalues of Qua(n, q) are computed, ...

In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite dimensional and it is dual to the the Bergman space on the pseudoconvex domain Ω−. The duality is further identified e...

We discover a Ising-type duality in the general N -state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N = 2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small k) to those of another chiral Potts model at a high temperature (of k). The τ -model and chiral Potts model on the dual lattice are establish...