7,213 research outputs found
On orbital variety closures in sl(n). II. Descendants of a Richardson orbital variety
For a semisimple Lie algebra g the orbit method attempts to assign
representations of g to (coadjoint) orbits in g*. Orbital varieties are
particular Lagrangian subvarieties of such orbits leading to highest weight
representations of g. In sl(n) orbital varieties are described by Young
tableaux. In this paper we consider so called Richardson orbital varieties in
sl(n). A Richardson orbital variety is an orbital variety whose closure is a
standard nilradical. We show that in sl(n) a Richardson orbital variety closure
is a union of orbital varieties. We give a complete combinatorial description
of such closures in terms of Young tableaux.
This is the second paper in the series of three papers devoted to a
combinatorial description of orbital variety closures in sl(n) in terms of
Young tableaux.Comment: 27 pages, to appear in Journal of Algebr
Inverse scattering of Canonical systems and their evolution
In this work we present an analogue of the inverse scattering for Canonical
systems using theory of vessels and associated to them completely integrable
systems. Analytic coefficients fits into this setting, significantly expanding
the class of functions for which the inverse scattering exist. We also derive
an evolutionary equation, arising from canonical systems, which describes the
evolution of the logarithmic derivative of the tau function, associated to
these systemsComment: arXiv admin note: substantial text overlap with arXiv:1303.532
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