86 citations · 478 across the 67 of their papers we have counts for
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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=…
Defining relations for the exceptional Lie superalgebras of vector fields pertaining to The Standard Model
Pavel Grozman, Dimitry Leites, Irina Shchepochkina
We list defining relations for the four of the five exceptional simple Lie superalgebras some of which, as David Broadhurst conjectured and Kac demonstrated, may pertain to The Sta…
The Index Theorem for Homogeneous Differential Operators on Supermanifolds
Dimitry Leites
In mid 60s Bott proved that (1) the index theorem for homogeneous, G-invariant, elliptic differential operators acting in the spaces of sections of induced representations of G ove…
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…