4 citations · 11 across the 9 of their papers we have counts for
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Bounded generalized Harish-Chandra modules
Ivan Penkov, Vera Serganova
Let be a complex reductive Lie algebra and $\kk\subset\gg$ be any reductive in subalgebra. We call a $(\gg,\kk)$-module bounded if the $\kk$-multiplicities of a…
Rank 2 vector bundles on ind-Grassmannians
Ivan Penkov, Alexander S. Tikhomirov
The simplest example of an ind-Grassmannian is the infinite projective space . The Barth-Van de Ven-Tyurin (BVT) Theorem, proved more than 30 years ago \cite{BV},…
Tensor representations of classical locally finite Lie algebras
I. Penkov, K. Styrkas
We study the structure of tensor representations of the classical infinite-dimensional locally finite Lie algebras , , and . In contras…
Triviality of vector bundles on sufficiently twisted ind-Grassmannians
Ivan Penkov, Alexander S. Tikhomirov
Twisted ind-Grassmannians are ind-varieties $\GG$ obtained as direct limits of Grassmannians , for $m\in\ZZ_{>0}$, under embeddings $ϕ_m:G(r_m,V^{r_m})\to G(r_{m+1}…
A construction of generalized Harish-Chandra modules for locally reductive Lie algebras
Ivan Penkov, Gregg Zuckerman
We study cohomological induction for a pair , being an infinite dimensional locally reductive Lie algebra and being of the for…