26 citations · 148 across the 44 of their papers we have counts for
7 papers · 1 filter
Higher Dirac cohomology of modules with generalized infinitesimal character
Pavle Pandžić, Petr Somberg
We modify the definition of Dirac cohomology in such a way that the standard properties of the usual Dirac cohomology, valid for modules with infinitesimal character, become valid…
Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry
P. Somberg
For a finite reflection subgroup $G\leq O(n+1,1,\mR)$ of the conformal group of the sphere with standard conformal structure , we geometrically derive differential-dif…
Branching laws for Verma modules and applications in parabolic geometry. I
Toshiyuki Kobayashi, Bent Ørsted, Petr Somberg +1
We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion fo…
Symplectic twistor operator on and the Segal-Shale-Weil representation
Marie Dostálová, Petr Somberg
The aim of our article is the study of solution space of the symplectic twistor operator in symplectic spin geometry on standard symplectic space , whic…
The F-method and a branching problem for generalized Verma modules associated to $({\LieGtwo},{so(7)})$
Todor Milev, Petr Somberg
The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in \cite{ms}. In the p…
Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally invariant differential operators
Petr Somberg
Based on the Lie theoretical methods of algebraic Fourier transformation, we classify in the case of generic values of inducing parameters the scalar singular vectors corresponding…