8 citations · 17 across the 4 of their papers we have counts for
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On unconventional integrations and cross ratio on supermanifolds
Dimitry Leites
The conventional integration theory on supermanifolds had been constructed so as to possess (an analog of) Stokes' formula. In it, the exterior differential d is vital and the inte…
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…
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…