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In a previous article the second author together with A. Pasquale determined the spectrum of the $Cos^lambda$ transform on smooth functions on the Grassmann manifolds $G_{p,n+1}$. This article extends those results to line bundles over certain Grassmannians. In particular we define the $Cos^lambda$ transform on smooth sections of homogeneous line bundles over$G_{p,n+1}$ and show that it is an intertwining operator between generalized ($chi$-spherical) principal series representations induced from a maximal parabolic subgroup of $mathrm{SL} (n+1, mathbb{K})$. Then we use the spectrum generating method to determine the $K$-spectrum of the $Cos^lambda$ transform.
We study a class of Poisson-Nijenhuis systems defined on compact hermitian symmetric spaces, where the Nijenhuis tensor is defined as the composition of Kirillov-Konstant-Souriau symplectic form with the so called Bruhat-Poisson structure. We determi
We review the projective-superspace construction of four-dimensional N=2 supersymmetric sigma models on (co)tangent bundles of the classical Hermitian symmetric spaces.
We prove a gap rigidity theorem for diagonal curves in irreducible compact Hermitian symmetric spaces of tube type, which is a dual analogy to a theorem obtained by Mok in noncompact case. Motivated by the proof we give a theorem on weaker gap rigidity problems for higher dimensional submanifolds.
Using Szenes formula for multiple Bernoulli series we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.
It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite dimensional inner product spaces. The representations, and the induced bundles, have composition