Harmonics on Stiefel manifolds and generalized Hankel transforms

Harmonics on Stiefel Manifolds and Generalized Hankel Transforms

In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...

Generalized Catalan Numbers, Hankel Transforms and Somos-4 Sequences

We study families of generalized Catalan numbers, defined by convolution recurrence equations. We explore their relations to series reversion, Riordan array transforms, and in a special case, to Somos-4 sequences via the mechanism of the Hankel transform.

Rolling Stiefel manifolds

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

Notes on Optimization on Stiefel Manifolds

On some generalized recurrent manifolds

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...