PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 82 | 1 | 49-63
Tytuł artykułu

Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.
Słowa kluczowe
Rocznik
Tom
82
Numer
1
Strony
49-63
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-03-19
Twórcy
  • Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, U.S.A.
Bibliografia
  • [1] N. Bergeron and F. Sottile, A Pieri-type formula for isotropic flag manifolds, math.CO/9810025, 1999.
  • [2] C. Chevalley, Sur les décompositions cellulaires des espaces G/B, in: Algebraic Groups and their Generalizations: Classical Methods, W. Haboush (ed.), Proc. Sympos. Pure Math. 56, Part 1, Amer. Math. Soc., 1994, 1-23.
  • [3] V. Deodhar, On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells, Invent. Math. 79 (1985), 499-511.
  • [4] W. Fulton, Intersection Theory, Ergeb. Math. Greuzgeb. 2, Springer, 1984.
  • [5] W. Fulton, Young Tableaux, Cambridge Univ. Press, 1997.
  • [6] W. Fulton and P. Pragacz, Schubert Varieties and Degeneracy Loci, Lecture Notes in Math. 1689, Springer, 1998.
  • [7] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, 1978.
  • [8] H. Hiller and B. Boe, Pieri formula for $SO_{2n+1}/U_n$ and $Sp_n/U_n$, Adv. Math. 62 (1986), 49-67.
  • [9] W. V. D. Hodge, The intersection formula for a Grassmannian variety, J. London Math. Soc. 17 (1942), 48-64.
  • [10] W. V. D. Hodge and D. Pedoe, Methods of Algebraic Geometry, Vol. II, Cambridge Univ. Press, 1952.
  • [11] S. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287-297.
  • [12] P. Pragacz, Algebro-geometric applications of Schur S- and Q-polynomials, in: Topics in Invariant Theory, Lecture Notes in Math. 1478, Springer, 1991, 130-191.
  • [13] P. Pragacz and J. Ratajski, Pieri type formula for isotropic Grassmannians; the operator approach, Manuscripta Math. 79 (1993), 127-151.
  • [14] P. Pragacz and J. Ratajski, Pieri-type formula for Lagrangian and odd orthogonal Grassmannians, J. Reine Angew. Math. 476 (1996), 143-189.
  • [15] P. Pragacz and J. Ratajski, A Pieri-type theorem for even orthogonal Grassmannians, Max-Planck Institut preprint, 1996.
  • [16] S. Sertöz, A triple intersection theorem for the varieties $SO(n)/P_d$, Fund. Math. 142 (1993), 201-220.
  • [17] F. Sottile, Pieri's formula for flag manifolds and Schubert polynomials, Ann. Inst. Fourier (Grenoble) 46 (1996), 89-110.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv82i1p49bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.