Remarks on Cauchy’s integral formula in matric spaces

Remarks on Catjchy's Integral Formula in Matric Spaces

Remarks on Fermionic Formula

Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the fermionic formulae associated with general non-twisted quantum affine algebra Uq(X (1) n ) and discuss several aspects related to representation theories and combinatorics. They include crystal base theor...

Remarks on Finite Subset Spaces

This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex X including their connectivity and manifold structure. It also discusses the inclusion of the singletons into the threefold subset space and shows that this subspace is weakly contractible but generally non-contractible unless X is a cogroup. Some homological calculati...

Some Remarks on Configuration Spaces

This paper studies the homotopy type of the configuration spaces Fn(X) by introducing the idea of configuration spaces of maps. For every map f : X → Y , the configuration space Fn(f) is the space of configurations in X that have distinct images in Y . We show that the natural maps Fn(X) ← Fn(f) → Fn(Y ) are homotopy equivalences when f is a proper cell-like map between d-manifolds. We also sho...

Remarks on some interpolation spaces

One purpose of this paper is to introduce a new idea of associating microlocal measures to bounded functions of bounded variation, and even to functions in the interpolation space (H(Q)yL (Q))1.7oo, in order to replace and improve some methods from geometric measure theory. Some properties of similar interpolation spaces are reviewed first. I do not remember when I met Enrico MAGENES for the fi...