We evaluate partition functions ZI in topologically nontrivial (instanton) gauge sectors in the bosonized version of the Schwinger model and in a gauged WZNW model corresponding to QCD2 with adjoint fermions. We show that the bosonized model is equivalent to the fermion model only if a particular form of the WZNW action with gauge-invariant integrand is chosen. For the exact correspondence, it ...

A normal complex algebraic variety X is called a symplectic variety (cf. [Be]) if its regular locus Xreg admits a holomorphic symplectic 2-form ω such that it extends to a holomorphic 2-form on a resolution f : X̃ → X. Affine symplectic varieties are constructed in various ways such as nilpotent orbit closures of a semisimple complex Lie algebra (cf. [CM]), Slodowy slices to nilpotent orbits (cf...

We give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(C_{omega_1,varphi_1}^*‎ , ‎C_{omega_2,varphi_2}^*)$ on the Hilbert space $mathcal{H}$ of analytic functions is supercyclic‎.

It is shown that projectivized irreducible components of nilpotent cones of complex symmetric spaces are projective self-dual algebraic varieties. Other properties equivalent to their projective self-duality are found. 1. Let g be a semisimple complex Lie algebra, let G be the adjoint group of g, and let θ ∈ Aut g be an element of order 2. We set k := {x ∈ g | θ(x) = x}, p := {x ∈ g | θ(x) = −x...

We propose a rigorous procedure to obtain the adjoint-based gradient representation of cost functionals for the optimal control of discontinuous solutions of conservation laws. Hereby, it is not necessary to introduce adjoint variables for the shock positions. Our approach is based on stability properties of the adjoint equation. We give a complete analysis for the case of convex scalar conserv...

This paper analyzes the adjoint solution of the Navier-Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ReD = 20, 100 and 500. The quantity of interest in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyze the adjoint solution, which is a vector field similar to a flow field. Production and dissipati...

We show that the sum of two adjoint orbits in the Lie algebra of an exponential Lie group coincides with the Campbell-Baker-Hausdorff product of these two orbits. Introduction N. Wildberger and others have recently investigated the structure of the hypergroup of the adjoint orbits in relation with the class hypergroup of compact Lie groups. A generalization of the notion of this type of hypergr...

It was observed in [Su5] that the spectrum of a periodic Schrodinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only f...