51 research outputs found
On the structure of Verma module over Virasoro and Neveu-Schwarz algebras
In the paper we present a different proof of the theorem of B. L. Feigin and
D. B. Fuchs about the structure of Verma modules over Virasoro algebra. We
state some new results about the structure of Verma modules over Neveu-Schwarz.
The proof has thwo advantages: first, it is simplier in the most interesting
cases (for example in the so called minimal models), second, it can be
generalized for Neveu-Schwarz algebra for some class of Verma modules.Comment: 41 pages, LaTe
Exotic Differential Operators on Complex Minimal Nilpotent Orbits
Let O be the minimal nilpotent adjoint orbit in a classical complex
semisimple Lie algebra g. O is a smooth quasi-affine variety stable under the
Euler dilation action on g. The algebra of differential operators on O is
D(O)=D(Cl(O)) where the closure Cl(O) is a singular cone in g. See \cite{jos}
and \cite{bkHam} for some results on the geometry and quantization of O.
We construct an explicit subspace of commuting
differential operators which are Euler homogeneous of degree -1. The space
is finite-dimensional, g-stable and carries the adjoint
representation. consists of (for ) non-obvious order
4 differential operators obtained by quantizing symbols we obtained previously.
These operators are "exotic" in that there is (apparently) no geometric or
algebraic theory which explains them. The algebra generated by is a
maximal commutative subalgebra A of D(X). We find a G-equivariant algebra
isomorphism R(O) to A, , such that the formula defines a positive-definite Hermitian inner product on
R(O).
We will use these operators to quantize O in a subsequent paper.Comment: 34 pages, corrected some typos, changed conten
On noncommutative Nahm transform
Motivated by the recently observed relation between the physics of -branes
in the background of -field and the noncommutative geometry we study the
analogue of Nahm transform for the instantons on the noncommutative torus.Comment: Latex, 22 p
On parabolic Whittaker functions
We derive a Mellin-Barnes integral representation for solution to generalized
(parabolic) quantum Toda lattice introduced in \cite{GLO}, which presumably
describes the -equivariant Gromov-Witten invariants of
Grassmann variety.Comment: 14 page
A note on bosonic open strings in constant B field
We sketch the main steps of old covariant quantization of bosonic open
strings in a constant field background. We comment on its space-time
symmetries and the induced effective metric. The low-energy spectrum is
evaluated and the appearance of a new non-commutative gauge symmetry is
addressed.Comment: 13 pages, Latex, important comments added, to appear in PR
Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism
The massless 4-point one-loop amplitude computation in the pure spinor
formalism is shown to agree with the computation in the RNS formalism.Comment: 10 pages harvmac te
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