The construction of cyclic codes can be generalized to so-called ”module θ-codes” using noncommutative polynomials. The product of the generator polynomial g of a self-dual ”module θ-code” and its ”skew reciprocal polynomial” is known to be a noncommutative polynomial of the form X − a, reducing the problem of the computation of all such codes to the resolution of a polynomial system where the ...

We define the dual of a set of generators of the fundamental group of an oriented two-surface S g,n of genus g with n punctures and the associated surface S g,n \D with a disc D removed. This dual is another set of generators related to the original generators via an involution and has the properties of a dual graph. In particular, it provides an algebraic prescription for determining the inter...

or its invariant space Inv(V1 ⊗ V2 ⊗ . . .⊗ Vn). The quantum group Uq(g) has representations and vector spaces of invariants which generalize these, and one can also study their bases, with or without the intention of specializing to q = 1. (For simplicity, we will usually consider Uq(g) as an algebra over C(q ), and we will only occassionally mention Z[q] as a ground ring.) Lusztig’s remarkabl...

A geodesic lamination L on a closed hyperbolic surface S, when provided with a transverse measure μ, gives rise to a “dual R-tree” Tμ, together with an action of G = π1S on Tμ by isometries. A point of Tμ corresponds precisely to a leaf of the lift L̃ of L to the universal covering S̃ of S, or to a complementary component of L̃ in S̃. The G-action on T is induced by the G-action on S̃ as deck transf...

We give an elementary proof of the following result: If G is a compact non-zero Abelian group with dual isomorphic to a subgroup of Q, such that U u (U) = G \ G(2) and U n (U) = 0 for some open subset U c G, where G(2) = {a E G: 2a = O}, then G is topologically isomorphic with T.

This paper is a brief survey of momentum maps, dual pairs and reduction in deformation quantization. We recall the classical theory of momentum maps in Poisson geometry and present its quantum counterpart. We also discuss quantization of momentum maps and applications of quantum momentum maps to quantum versions of Marsden-Weinstein reduction. This paper is organized as follows. We recall the c...

For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...

1.1. Let G be a simply connected semisimple group with Borel subgroup B, N = [B,B] and let H = B/N . Let g, b, n and h be the respective Lie algebras of these groups. Let G be the Langlands dual group with dual Borel B, etc. Let X be a smooth curve or the formal disc D or the formal punctured disc D×. 1.2. Recall that a g-oper over X is a G-bundle FLG = F with a reduction FLB to B and a connect...