Hilbert functions of points on Schubert varieties in the Symplectic Grassmannian
# Hilbert functions of points on Schubert varieties in the Symplectic Grassmannian

### Sudhir R. Ghorpade

#### *
Department of Mathematics *

Indian Institute of Technology Bombay

Powai, Mumbai 400076, India

E-Mail: srg@math.iitb.ac.in

### and

### K. N. Raghavan

#### *
Institute of Mathematical Sciences *

C.I.T. Campus, Taramani

Chennai 600013, India

E-Mail: knr@imsc.ernet.in

## Abstract

We give an explicit combinatorial description of the multiplicity as well as
the Hilbert function of the tangent cone at any point on a Schubert variety
in the symplectic Grassmannian.

Contents

1 | Introduction | 1 |

2 | The Theorem | 3 |

3 | Reduction to Combinatorics | 5 |

4 | Further Reductions | 10 |

5 | Completion of Proof | 13 |

6 | Interpretations | 18 |

| References | 22 |

This paper is published in the
*Transactions of the American
Mathematical Society*, Vol. 358, No. 12 (2006), pp. 5401-5423.

See the Abstract, references and article information maintained by the journal.

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