A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed deformation parameter q ∈ C \ {0} exactness is proven for all q which are not a root of un...

We consider analogues of the Bernstein–Gelfand–Gelfand resolution in a highest weight category P♡. prove resulting complexes is chain-level lift heart constructible t-structure on its bounded derived P. In particular, an object admits Bernstein-Gelfand-Gelfand if and only certain Ext vanishing with costandard objects holds. These results appear to be new even for Category O.

In this paper, we deal with the inverse spectral problem for the equation −(pu′)′ + qu = λρu on a finite interval (0, h). We give some uniqueness results on q and ρ from the Gelfand spectral data, when the coefficients p and ρ are piecewise Lipschitz and q is bounded. We also prove an equivalence result between the Gelfand spectral data and the Borg–Levinson spectral data. As a consequence, we ...

We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous non-cutoff Boltzmann equation with Maxwellian molecules enjoys the same Gelfand-Shilov regularizing effect as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator.

Gelfand-Graev characters and their degenerate counterparts have an important role in the representation theory of finite groups of Lie type. Using a characteristic map to translate the character theory of the finite unitary groups into the language of symmetric functions, we study degenerate Gelfand-Graev characters of the finite unitary group from a combinatorial point of view. In particular, ...

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

This thesis gives an introduction to the study of Gelfand pairs and their applications. We begin with a brief introduction to the notion of a Gelfand pair and then move to some of the foundational results concerning Gelfand pairs. Next, we explore specific examples of Gelfand pairs, developing tools of independent interest as we progress. We find that consideration of a specific example of a Ge...

We consider functional Schrödinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional symbolic calculus allows to prove the convergence of the corresponding Hamiltonian Feynman integrals for propagators of coherent states...