86 citations · 478 across the 67 of their papers we have counts for
8 papers · 2 filters
Invariant operators on supermanifolds and Standard Models
Pavel Grozman, Dimitry Leites, Irina Shchepochkina
Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for opera…
The Riemann tensor for nonholonomic manifolds
Dimitry Leites
For every nonholonomic manifold, i.e., manifold with nonintegrable distribution, the analog of the Riemann tensor is introduced. It is calculated here for the contact and Engel str…
On unconventional integrations and cross ratio on supermanifolds
Dimitry Leites
(A) The conventional integration theory on supermanifolds had been constructed in order to have (an analog of) the Stokes formula in which a~sub-supermanifold is of codimension $1=…
Indecomposable representations of Lie superalgebras
Dimitry Leites
In 1960's I. Gelfand posed a problem: describe indecomposable representations of any simple infinite dimensional Lie algebra of polynomial vector fields. Here, by applying the elem…
The Howe duality and Lie superalgebras
Dimitry Leites, Irina Shchepochkina
Howe's duality is considered from a unifying point of view based on Lie superalgebras. New examples are offered. In particular, we construct several simplest spinor-oscillator repr…
Casimir operators for Lie superalgebras
Dimitry Leites, Alexander Sergeev
Casimir operators -- the generators of the center of the enveloping algebra -- are described for simple or close to them ``classical'' finite dimensional Lie superalgebras with non…