where k (p) is the +1 (−1) eigenspace of θ on g. Let Z(g) be the center of the universal enveloping algebra of g, and fix a character χ of Z(g). Let HC be the category of Harish-Chandra modules for G (i.e. finitely generated (g,K)–modules), and let HCχ be the full subcategory of HC of the modules with generalized central character χ. We are interested in the distribution characters, say, of the...

We give a nonstandard variant of Jordan’s proof of the Jordan curve theorem which is free of the defects his contemporaries criticized and avoids the epsilontic burden of the classical proof. The proof is selfcontained, except for the Jordan theorem for polygons taken for granted.

The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G2 i ↪→ so(7), and generalized conformal so(7)-Verma modules of scalar type. As a result, we classify t...

The goal of this short paper is to give a slightly different perspective on the comparison between crystalline cohomology and de Rham cohomology. Most notably, we reprove Berthelot’s comparison result without using pd-stratifications, linearisations, and pd-differential operators. Crystalline cohomology is a p-adic cohomology theory for varieties in characteristic p created by Berthelot [Ber74]...

Let X and Y be Hilbert C∗-modules over a C∗-algebra, and φ : X ×Y → [0,∞) be a function. A (not necessarily linear) mapping f : X → Y is called a φ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that ‖〈f(x), y〉 − 〈x, g(y)〉‖ ≤ φ(x, y) (x ∈ X , y ∈ Y). In this paper, we investigate the generalized Hyers–Ulam–Rassias stability of adjointable mapping...

We provide a necessary and sufficient condition for type D Temperley-Lieb algebra TLDn(δ) being semi-simple by studying branching rule cell modules. As byproduct, our result is used to study the so-called forked algebra, which quotient of TLDn(δ).

The linear δ expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear δ expansion for 〈~ φ 〉 converges, with errors decreasing like a power of the order n in δ. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors see...

In this paper, we compute Gram determinants associated to all cell modules of Brauer algebras Bn(δ). Theoretically, we know when a cell module of Bn(δ) is equal to its simple head. This gives a solution of this long standing problem. On the occasion of Professor Gus Lehrer’s 60 birthday

For the Auslander algebras E of self-injective Nakayama algebras, the Δ-filtrations of the submodules of indecomposable projective Emodules are determined, a class of Δ-filtered E-modules without selfextensions are constructed, and the Ringel dual of E is described. Mathematics Subject Classifications: 16G10