32 citations · 42 across the 4 of their papers we have counts for
8 papers
A formula for K-theory truncation Schubert calculus
Allen Knutson, Alexander Yong
Define a ``truncation'' of a polynomial in as the polynomial with all but the first variables set to zero. In certain good cases, the trunc…
Subword complexes in Coxeter groups
Allen Knutson, Ezra Miller
Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σand an element in Πdetermine a {\em subword complex}, as introduced in our paper on Gröbner geometry of Schubert poly…
Four positive formulae for type A quiver polynomials
Allen Knutson, Ezra Miller, Mark Shimozono
We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton. All four formulae are combinatorial, in the sense that they are expressed in ter…
A Schubert calculus recurrence from the noncomplex W-action on G/B
Allen Knutson
In this paper, as in our previous "Descent-cycling in Schubert calculus" math.CO/0009112, we study the structure constants in equivariant cohomology of flag manifolds G/B. In this…
The symplectic and algebraic geometry of Horn's problem
Allen Knutson
Horn's problem was the following: given two Hermitian matrices with known spectra, what might be the eigenvalue spectrum of the sum? This linear algebra problem is exactly of the s…
A limit of toric symplectic forms that has no periodic Hamiltonians
Jean-Claude Hausmann, Allen Knutson
We calculate the Riemann-Roch number of some of the pentagon spaces defined in [Klyachko,Kapovich-Millson,HK1]. Using this, we show that while the regular pentagon space is diffeom…