By Alex Eskin, Andrei Okounkov (auth.), Victor Ginzburg (eds.)

One of the main inventive mathematicians of our occasions, Vladimir Drinfeld got the Fields Medal in 1990 for his groundbreaking contributions to the Langlands software and to the speculation of quantum groups.

These ten unique articles through well known mathematicians, devoted to Drinfeld at the get together of his fiftieth birthday, commonly replicate the variety of Drinfeld's personal pursuits in algebra, algebraic geometry, and quantity theory.

Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman.

Show description

Read Online or Download Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld’s 50th Birthday PDF

Similar geometry and topology books

Relativite, groupes et topologie II: Les Houches, session XL, 27 juin-4 aout 1983 = Relativity, groups, and topology II

The classes which contain this ebook have been designed to offer the scholar a huge point of view on sleek quantum box idea. one of the themes coated are: - an account of the quantum concept of the Yang-Mills box, anomalies, monopoles and o-vacua; - an exposition of history box and Green's functionality innovations utilized to conservation legislation, practical integration, curved backgrounds, nontrivial topologies and the powerful motion; - an outline of supergravity and Kaluza-Klein theories; - supermanifolds, large Lie teams and tremendous Hilbert areas and thought of the topological and international features of quantum concept; - proofs of the confident power theorems, and - bills and research of episodes within the historical past of theoretical physics and quantum box thought.

Lectures on Low-Dimensional Topology (Monographs in Geometry & Topology)

In the course of the week of could 18-26, 1992, a convention on low-Dimensional Topology was once held on the collage of Tennessee, Knoxville. The convention was once dedicated to a wide spectrum of issues in Low-Dimensional Topology. although, specific emphasis was once given to hyperbolic and combinatorial constructions, minimum floor concept, negatively curbed teams, team activities on R-trees, and gauge theoretic facets of 3-manifolds.

Additional info for Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld’s 50th Birthday

Sample text

The images of evα , evα¯ , ev∅ and the union of the images of evαα ¯ and evα α¯ are pairwise disjoint. The complement to their union in the whole group is of codimension two. It consists of the antidiagonal matrices. 7. The images of evα , evα¯ , ev∅ are Poisson subvarieties with respect to the standard Drinfeld–Jimbo Poisson–Lie structure on PGL(2, C). The Poisson bracket is given by {z0 , z1 } = z0 z1 ; {w0 , w1 } = w0 w1 . In the above constructions one can replace C× by Gm , PGL(2, C) by the group scheme PGL(2), and upgrade all maps to the maps of the corresponding schemes.

Xn ) = 1 Z(∅, ∅; q) (29) × [y10 · · · yn0 ] tr q H ψ(x1 y1 )ψ ∗ (y1 ) · · · ψ(xn yn )ψ ∗ (yn )W. 2 By the main result of [9], we have w(λ) ≤ 1 (30) for any partition λ. In other words, all diagonal matrix elements of W are bounded by 1. For the off-diagonal elements, we prove the following cruder bound. Proposition 3. Let M = max{|λ|, |µ|}. Then ⎛ ⎜1 (Wvλ , vµ ) ≤ exp ⎝ 2 M−1 2 n=0 ⎞ 1 ⎟ 1/4 ⎠ ∼ const · M . 2n + 1 (31) To see this note that (Wvλ , vµ ) = (W[M] vλ , vµ ), where W[M] is the truncated operator ⎛ ⎞ ⎛ α−2n−1 ⎠ exp ⎝ exp ⎝− 2n + 1 2n+1≤M ⎞ 2n+1≤M α2n+1 ⎠ .

If Cαβ = −3, Cβα = −1, then αα → α. αβ → βα. αβα → βαβ. Eα H α (x)Eβ H β (y)Eα H α (z)Eβ H β (w)Eα Eβ = H β (a )H α (b )Eβ H β (y )Eα H α (x )Eβ H β (w )Eα H α (z )Eβ H β (q )Eα H α (p ), (13) where a , b , x , y , z , w , p , q are rational functions of x, y, z, w given by (24). Further, one has αα ¯ → α α. ¯ ⎛ Fα H α (x)Eα = ⎝ β=α ⎞ H β (1 + x)−Cαβ⎠H α (1+x −1 )−1 Eα H α (x −1 )Fα H α (1+x −1 )−1 . 46 V. V. Fock and A. B. Goncharov αβ ¯ → β α. ¯ Fα Eβ = Eβ Fα if α = β. Applying the antiautomorphism of g which acts as the identity on the Cartan subalgebra, and interchanges Fα and Eα , we obtain similar formulas for α¯ α¯ → α, ¯ α¯ β¯ → β¯ α, ¯ α¯ β¯ α¯ → β¯ α¯ β¯ and α¯ β¯ α¯ β¯ → β¯ α¯ β¯ α.

Download PDF sample

Rated 4.67 of 5 – based on 24 votes