Niveau: Supérieur, Doctorat, Bac+8
HAIMANS WORK ON THE N ! THEOREM, AND BEYOND IAIN GORDON Contents Introduction 2 Lecture 1 3 1.1. Symmetric functions and the Frobenius map 3 1.2. Plethysm 5 1.3. Macdonald polynomials 6 1.4. The Garsia-Haiman model 7 Lecture 2 9 2.1. The one variable case 9 2.2. The two variable case 11 2.3. Here comes the Hilbert scheme 12 2.4. Outline of proof of Haiman's big theorem 14 Lecture 3 16 3.1. Identifying FRµ(z; q, t) and H˜µ(z; q, t) 16 3.2. Homological consequences of Hn = Hilb Sn(C2n) 18 3.3. Polygraphs revisited 19 3.4. The zero fibre Zn ? Hn 21 Lecture 4 22 4.1. Diagonal coinvariants 22 4.2. New proofs 23 4.3. Beyond Sn: coinvariants 24 4.4. Beyond Sn: symmetric functions 25 4.5. Beyond Sn: geometry 26 References 28 I thank Michel Brion for the opportunity to give these lectures in Grenoble, and the participants of the summer school for their comments. 1
- inner product
- function theory
- h?1h?2 ·
- symmetric functions
- haimans work
- let ?
- natural spaces
- commuting variables
- variables seemed