# A Double Hall Algebra Approach to Affine Quantum Schur-Weyl by Bangming Deng

By Bangming Deng

Best algebra & trigonometry books

An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra

During this advent to commutative algebra, the writer choses a path that leads the reader in the course of the crucial principles, with out getting embroiled in technicalities. he's taking the reader fast to the basics of advanced projective geometry, requiring just a simple wisdom of linear and multilinear algebra and a few hassle-free workforce concept.

Inequalities : a Mathematical Olympiad approach

This publication is meant for the Mathematical Olympiad scholars who desire to organize for the examine of inequalities, a subject now of common use at a variety of degrees of mathematical competitions. during this quantity we current either vintage inequalities and the extra priceless inequalities for confronting and fixing optimization difficulties.

Recent Progress in Algebra: An International Conference on Recent Progress in Algebra, August 11-15, 1997, Kaist, Taejon, South Korea

This quantity provides the complaints of the foreign convention on ""Recent growth in Algebra"" that was once held on the Korea complicated Institute of technological know-how and know-how (KAIST) and Korea Institute for complex learn (KIAS). It introduced jointly specialists within the box to debate growth in algebra, combinatorics, algebraic geometry and quantity idea.

Extra info for A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory

Sample text

3) The proof above can be easily modified to construct a C-algebra isomorphism EH,C : D ,C (n) → UC (gln ), where the algebras are defined over C with respect to a non-root-of-unity z ∈ C∗ .

1) is defined over A. Hence, we can form a double Ringel–Hall algebra D (n)A . Then D ,C (n) ∼ = D (n)A ⊗ C and D (n) = D (n)A ⊗ Q(v). 2. Schiffmann–Hubery generators In this and the following sections, we will investigate the structure of D (n) by relating it with the quantum enveloping algebra of a generalized Kac–Moody algebra based on [67, 39]; see also [38, 14]. 1). Recall that an element of a Hopf algebra with comultiplication is called primitive if 38 2. Double Ringel–Hall algebras of cyclic quivers (x) = x ⊗ 1 + 1 ⊗ x.

Also, let U(gln )0 be i,0 , εn , θ−s ), for 1 the subalgebra of U(gln ) generated by the ki±1 . 1) induces that of U(gln ). 4. The multiplication map U(gln )+ ⊗ U(gln )0 ⊗ U(gln )− −→ U(gln ) is a Q(v)-space isomorphism. 5. 12)]. Indeed, under the isomorphism EH , C is identified with the central subalgebra Z (n) of D (n). (2) In [40] a Hopf algebra isomorphism H (n) 0 → U(gln )+ ⊗ U(gln )0 −1 was established and, moreover, the elements EH−1 (x+j,−1 k−1 j ) and EH (gi,±s ) in D (n) were explicitly described.