skip to main content

Explore Research Products in the NSF-PAR

  • Home
  • Search Results
  • Page 1 of 2

Search for: All records

Award ID contains: 1665239

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ( , Arnold Mathematical Journal)
    null (Ed.)
    We consider the KZ differential equations over C in the case, when the hypergeometric solutions are one-dimensional integrals.We also consider the same differential equations over a finite field F_p. We study the space of polynomial solutions of these differential equations over F_p, constructed in a previous work by Schechtman and the second author. Using Hasse–Witt matrices, we identify the space of these polynomial solutions over F_p with the space dual to a certain subspace of regular differentials on an associated curve. We also relate these polynomial solutions over F_p and the hypergeometric solutions over C. 
    more » « less
    Full Text Available 
  2. ; ; ; ( , Symmetry, Integrability and Geometry: Methods and Applications)
    Full Text Available 
  3. ; ( , Journal of Geometry and Physics)
    null (Ed.)
    Full Text Available 
  4. ; ( , Symmetry integrability and geometry methods and applications)
    We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl2-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra sl2^. In [Schechtman V., Varchenko A., Mosc. Math. J. 17 (2017), 787-802] a construction of a monomorphism of the first complex to the second was suggested and it was indicated that under this monomorphism the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the de Rham complex. In this paper we prove these results. △ Less 
    more » « less
    Full Text Available 
  5. ; ; ( , Selecta Mathematica)
    Full Text Available 
  6. ; ( , The Ramanujan Journal)
    We construct polynomial solutions of the KZ differential equations over a finite field F_p as analogs of hypergeometric solutions. 
    more » « less
    Full Text Available 
  7. ; ( , Moscow Mathematical Journal)
    null (Ed.)
    Full Text Available 
  8. ; ; ( , Symmetry, Integrability and Geometry: Methods and Applications)
    Full Text Available 
  9. ; ; ( , Selecta Mathematica)
    Full Text Available 
  10. ; ( , Glasgow Mathematical Journal)
    Abstract This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame, which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the potentials, a power series ansatz is made. The proof that it works requires that certain decompositions of tuples of coordinate vector fields are related by certain elementary transformations. This is shown with a nontrivial result on matroid partition. 
    more » « less
    Full Text Available