Geodesic
On combinatorics of quiver component formulas
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 3, pp. 351-371.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Buch and Fulton [9] conjectured the nonnegativity of the quiver coefficients appearing in their formula for a quiver cycle. Knutson, Miller and Shimozono [24] proved this conjecture as an immediate consequence of their $ldquo$component formula $rdquo$. We present an alternative proof of the component formula by substituting combinatorics for Gröbner degeneration [23, 24]. We relate the component formula to the work of Buch, Kresch, Tamvakis and the author [10] where a $ldquo$splitting $rdquo$ formula for Schubert polynomials in terms of quiver coefficients was obtained. We prove analogues of this latter result for the type $B$CD-Schubert polynomials of Billey and Haiman [4]. The form of these analogues indicate that it should be interesting to pursue a geometric context that explains them.
Keywords: key words degeneracy loci, quiver polynomials, component formula, generalized Littlewood-Richardson coefficients 
@article{JAC_2005__21_3_a0,
     author = {Yong, Alexander},
     title = {On combinatorics of quiver component formulas},
     journal = {Journal of Algebraic Combinatorics},
     pages = {351--371},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2005__21_3_a0/}
}
TY  - JOUR
AU  - Yong, Alexander
TI  - On combinatorics of quiver component formulas
JO  - Journal of Algebraic Combinatorics
PY  - 2005
SP  - 351
EP  - 371
VL  - 21
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2005__21_3_a0/
LA  - en
ID  - JAC_2005__21_3_a0
ER  - 
%0 Journal Article
%A Yong, Alexander
%T On combinatorics of quiver component formulas
%J Journal of Algebraic Combinatorics
%D 2005
%P 351-371
%V 21
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2005__21_3_a0/
%G en
%F JAC_2005__21_3_a0
Yong, Alexander. On combinatorics of quiver component formulas. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 3, pp. 351-371. http://geodesic.mathdoc.fr/item/JAC_2005__21_3_a0/