文档介绍：A PIERI-TYPE FORMULA FOR ISOTROPIC FLAG MANIFOLDSNANTEL BERGERON AND FRANK SOTTILEAbstract. We give the formula for multiplying a Schubert class on an odd or-thogonal or symplectic ag manifold by a special Schubert class pulled back from aGrassmannian of maximal isotropic subspaces. This is also the formula for multiply-ing a type B (respectively, type C) Schubert polynomial by the Schur P-polynomialpm (respectively, the Schur Q-polynomial qm). Geometric constructions and inter-mediate results allow us to ultimately deduce this from formulas for the classicalag manifold. These intermediate results are concerned with the Bruhat order ofthe Coxeter group B1, identities of the structure constants for the Schubert basisof cohomology, and intersections of Schubert varieties. We show these identities fol-low from the Pieri-type formula, except some `hidden symmetries' of the structureconstants. Our analysis leads to a new partial order on the Coxeter group B1 andformulas for many of these structure 2 1. Statement of results 2 2. Orders on B1 8 . The 0-Bruhat order 9 . A monoid for the Lagrangian order 13 3. Isotropic ag manifolds and maximal Grassmannians 15 . Schubert varieties 16 4. Identities of structure constants 19 5. More identities 22 . Product position 22 . Some hidden symmetries 23 . More hidden symmetries 25 6. Minimal permutations and labeled reseaux 27 . Minimal permutations 27Date: 2 July Mathematics Subject Classi cation. 14M15, 05E15, 05E05, 06A07, words and phrases. Pieri formula, isotropic ag manifold, Bruhat order, Schubert variety,Lagrangian Grassmannian, Schubert polynomial, Schur P- author supported in part by NSERC and CRM author supported in part by NSERC grant OGP0170279 and NSF grant DMS- 2 NANTEL BERGERON AND FRANK . The Grassmann-Bruhat order on S1 29 . The labeled Lagrangian order 30 . The Lagrangian reseau 32 7. The Pie