8,798 research outputs found
Lie-algebraic discretization of differential equations
A certain representation for the Heisenberg algebra in finite-difference
operators is established. The Lie-algebraic procedure of discretization of
differential equations with isospectral property is proposed. Using
-algebra based approach, (quasi)-exactly-solvable finite-difference
equations are described. It is shown that the operators having the Hahn,
Charlier and Meixner polynomials as the eigenfunctions are reproduced in
present approach as some particular cases. A discrete version of the classical
orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is
introduced.Comment: 11 pages, LaTeX (a few enlightening remarks added, typos corrected
On residual categories for Grassmannians
We define and discuss some general properties of residual categories of
Lefschetz decompositions in triangulated categories. In the case of the derived
category of coherent sheaves on the Grassmannian we conjecture
that the residual category associated with Fonarev's Lefschetz exceptional
collection is generated by a completely orthogonal exceptional collection. We
prove this conjecture for , a prime number, modulo completeness of
Fonarev's collection (and for we check this completeness).Comment: Final version. To appear in PLM
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