146 citations · 484 across the 48 of their papers we have counts for
53 papers
Permutahedra, Lusztig varieties, degenerations, and subdivisions
Allen Knutson, Mario Sanchez, Melissa Sherman-Bennett
We present an embedded (in ) degeneration of Lusztig varieties (which generalize type Hessenberg varieties) to certain unions of Richardson varieties, giving a simultaneou…
Schubert puzzles and integrability III: separated descents
Allen Knutson, Paul Zinn-Justin
In paper I of this series we gave positive formulae for expanding the product of two Schubert polynomials, in the case that both had shared desce…
The Duistermaat-Heckman formula and Chern-Schwartz-MacPherson classes
Allen Knutson
Let M be a smooth complex projective variety, bearing a Kähler symplectic form ωand a Hamiltonian action of a torus T, with finitely many fixed points M^T. One standard form of the…
A Bruhat atlas for the Mehta-van der Kallen stratification of
Allen Knutson, Steven V Sam
Mehta and van der Kallen put a Frobenius splitting on the type A cotangent bundle , thereby defining a stratification by compatibly split subvarieties, and they determi…
Schubert puzzles and integrability II: multiplying motivic Segre classes
Allen Knutson, Paul Zinn-Justin
In Schubert Puzzles and Integrability I we proved several "puzzle rules" for computing products of Schubert classes in K-theory (and sometimes equivariant K-theory) of d-step flag…
Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula
Allen Knutson
We give a new proof that three families of polynomials coincide: the double Schubert polynomials of Lascoux and Schützenberger defined by divided difference operators, the pipe dre…