Modules over plane curve singularities in any ranks and DAHA

JOURNAL OF ALGEBRA

卷:520

Article

Cherednik, Ivan¹  Philipp, Ian¹ 

[1] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

关键词: Hecke algebra;    Khovanov-Rozansky homology;    Algebraic knot;    Macdonald polynomial;    Plane curve singularity;    Compactified Jacobian;    Puiseux expansion;    Orbital integral;   

DOI  :  10.1016/j.jalgebra.2018.11.006

来源: Elsevier

【 摘 要 】

We generalize the construction of geometric superpolynomials for unibranch plane curve singularities from our prior paper from rank one to any ranks; explicit formulas are obtained for torus knots. The new feature is the definition of counterparts of Jacobian factors (directly related to compactified Jacobians) for higher ranks, which is parallel to the classical passage from invertible sheaves to vector bundles over algebraic curves. This is an entirely local theory, connected with affine Springer fibers for non-reduced (germs of) spectral curves. We conjecture and justify numerically the connection of our geometric polynomials in arbitrary ranks with the corresponding DAHA superpolynomials for any algebraic knots colored by columns. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free