187 research outputs found
Tautological classes on the moduli space of hyperelliptic curves with rational tails
We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. (C) 2017 Elsevier B.V. All rights reserved11sci
Laurent family of simple modules over quiver Hecke algebra
We introduce the notions of quasi-Laurent and Laurent families of simple
modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove
that such a family plays a similar role of a cluster in the quantum cluster
algebra theory and exhibits a quantum Laurent positivity phenomenon for the
basis of the quantum unipotent coordinate ring
, coming from the categorification. Then we
show that the families of simple modules categorifying GLS-clusters are Laurent
families by using the PBW-decomposition vector of a simple module and
categorical interpretation of (co-)degree of . As applications of such
-vectors, we define several skew symmetric pairings on arbitrary
pairs of simple modules, and investigate the relationships among the pairings
and -invariants of R-matrices in the quiver Hecke algebra theory.Comment: 26 page
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