Browsing by Subject "Equivariant quantum differential equation"

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    Equivariant quantum differential equation, Stokes bases, and K-theory for a projective space
    (Springer, 2021-06) Tarasov, Vitaly; Varchenko, Alexander; Mathematical Sciences, School of Science
    We consider the equivariant quantum differential equation for the projective space $$P^{n-1}$$and introduce a compatible system of difference equations. We prove an equivariant gamma theorem for $$P^{n-1}$$, which describes the asymptotics of the differential equation at its regular singular point in terms of the equivariant characteristic gamma class of the tangent bundle of $$P^{n-1}$$. We describe the Stokes bases of the differential equation at its irregular singular point in terms of the exceptional bases of the equivariant K-theory algebra of $$P^{n-1}$$and a suitable braid group action on the set of exceptional bases. Our results are an equivariant version of the well-known results of Dubrovin and Guzzetti.