Poisson transforms adapted to BGG-complexes

Dual Bgg Complexes for Automorphic Bundles

We generalize the construction of dual BGG complexes in Faltings–Chai and Mokrane–Tilouine–Polo (from the case of Siegel modular varieties) to all smooth integral models of PEL-type Shimura varieties.

Hierarchies of Simplicial Complexes via the Bgg-correspondence

Via the BGG-correspondence a simplicial complex ∆ on [n] is transformed into a complex of coherent sheaves L̃(∆) on the projective space P. In general we compute the support of each of its cohomology sheaves. When the Alexander dual ∆ is Cohen-Macaulay there is only one such non-zero cohomology sheaf. By considering when this sheaf can be an a’th syzygy sheaf in a locally free resolution, we get...

Single-pass adapted training with all-pass transforms

In recent work, the all-pass transform (APT) was proposed as the basis of a speaker adaptation scheme intended for use with a large vocabulary speech recognition system. It was shown that APT-based adaptation reduces to a linear transformation of cepstral means, much like the better known maximum likelihood linear regression (MLLR), but is specified by far fewer free parameters. Due to its line...

Compact representation of images by edge adapted multiscale transforms

Axiomatic Framework for the Bgg

We present a general setup in which one can define an algebra with a regular triangular decomposition. This setup incorporates several important examples in representation theory, including semisimple, Kac-Moody, contragredient, and Borcherds Lie algebras, the Virasoro algebra, and quantum groups. In all these cases, the “Cartan” subalgebra is a commutative cocommutative Hopf algebra; we show t...