Results 41 to 50 of about 10,484 (179)

Double Schubert polynomials and degeneracy loci for the classical groups [PDF]

, 2002
We propose a theory of double Schubert polynomials P_w(X,Y) for the Lie types B, C, D which naturally extends the family of Lascoux of Schutzenberger in type A.
Kresch, Andrew, Tamvakis, Harry
core   +4 more sources

Balanced Labellings and Schubert Polynomials

European Journal of Combinatorics, 1997
By a diagram the authors mean a finite collection of cells in \({\mathbb Z}\times {\mathbb Z}\). They consider balanced labellings of diagrams. Special cases of these objects are the standard Young tableaux and the balanced tableaux introduced by \textit{P. Edelman} and \textit{C. Greene} [Adv. Math. 63, 42-99 (1987; Zbl 0616.05005)]. It turns out that
Fomin, Sergey, Greene, Curtis, Reiner, Victor, Shimozono, Mark   +3 more
openaire   +1 more source

Schubert Quiver Grassmannians [PDF]

, 2017
Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties.
CERULLI IRELLI, GIOVANNI, Feigin, Evgeny, Reineke, Markus   +2 more
core   +1 more source

Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial$ P_id,w(q)=1+q^h$ for
Alexander Woo
doaj   +1 more source

Sparse multivariate polynomial interpolation in the basis of Schubert polynomials

, 2016
Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials.
Mukhopadhyay, Priyanka, Qiao, Youming
core   +1 more source

Quantum bumpless pipe dreams

Forum of Mathematics, Sigma
Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams.
Tuong Le, Shuge Ouyang, Leo Tao, Joseph Restivo, Angelina Zhang   +4 more
doaj   +1 more source

Wonderful symmetric varieties and Schubert polynomials

Ars Mathematica Contemporanea, 2018
19 ...
Can, Mahir Bilen, Joyce, Michael, Wyser, Benjamin   +2 more
openaire   +5 more sources

Schubert polynomials and Arakelov theory of symplectic flag varieties

, 2013
Let X be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of X.
Tamvakis, Harry
core   +1 more source

Some Combinatorial Properties of Schubert Polynomials [PDF]

Journal of Algebraic Combinatorics, 1993
The main result of the Section 1 of the reviewed paper is to give an explicit combinatorial interpretation of the Schubert polynomial \({\mathfrak S}_ w\) in terms of the reduced decompositions of the permutation \(w\). This interpretation is completely different from an earlier conjecture of A. Kohnert and a theorem of N. Bergeron (see \textit{I.
Billey, Sara C., Jockusch, William, Stanley, Richard P.   +2 more
openaire   +2 more sources

Schubert polynomials for the classical groups [PDF]

Journal of the American Mathematical Society, 1995
We present a general theory of Schubert polynomials, which are explicit representatives for Schubert classes in the cohomology ring of a flag variety with certain combinatorial properties. The starting point for this theory is a construction of Schubert classes in the cohomology ring of the flag variety of any semi-simple complex Lie group by Bernstein-
Billey, Sara, Haiman, Mark
openaire   +1 more source