By Bangming Deng

ISBN-10: 1607092050

ISBN-13: 9781607092056

The speculation of Schur-Weyl duality has had a profound effect over many components of algebra and combinatorics. this article is unique in respects: it discusses affine q-Schur algebras and offers an algebraic, instead of geometric, method of affine quantum Schur-Weyl idea. to start, quite a few algebraic constructions are mentioned, together with double Ringel-Hall algebras of cyclic quivers and their quantum loop algebra interpretation. the remainder of the ebook investigates the affine quantum Schur-Weyl duality on 3 degrees. This contains the affine quantum Schur-Weyl reciprocity, the bridging function of affine q-Schur algebras among representations of the quantum loop algebras and people of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel-Hall algebra with an explanation of the classical case. this article is perfect for researchers in algebra and graduate scholars who are looking to grasp Ringel-Hall algebras and Schur-Weyl duality.

**Read Online or Download A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory PDF**

**Best algebra & trigonometry books**

**Technical Math For Dummies (For Dummies (Math & Science)) by Barry Schoenborn, Bradley Simkins PDF**

This ebook is like that first lick off a chocolate mint ice cream cone or the texture of the sea breeze in your face ; you simply gotta event it first hand to grasp why i bought over a dozen copies for each loved ones of my nieces and nephews, neighbors who support their childrens with math homework, K-12, and to a center college math instructor to remind him how math may be taught with ease with that means and entertainment.

**Get The Complexity of Boolean Functions (Wiley Teubner on PDF**

Provides quite a few contemporary learn effects formerly unavailable in booklet shape. in the beginning offers with the wee-known computation types, and is going directly to particular forms of circuits, parallel pcs, and branching courses. comprises uncomplicated thought besides contemporary examine findings. every one bankruptcy comprises workouts.

- Basic College Mathematics: A Text Workbook, 3rd Edition
- Unipotent Algebraic Groups
- Motives (Proceedings of Symposia in Pure Mathematics, Vol 55, Part 1)
- PI-Algebras: An introduction

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

**Sample text**

Fi /[m] , where i ∈ I , t 0, and s, m 1. Further, we set U + = U+ ∩ U , U − = U− ∩ U , and U 0 = U0 ∩ U . , ys and Fi ), for i ∈ I and s, m 1. Consequently, we obtain U + = U (sln )+ ⊗ Z[x1 , x2 , . ] and U − = U (sln )− ⊗ Z[y1 , y2 , . ], where U (sln )+ and U (sln )− are the Z-subalgebras of U(sln ) generated by (m) (m) the divided powers E i and Fi , respectively. This implies in particular that both U + and U − are free Z-modules. We now look at the structure of U 0 . Let V 0 be the Z-subalgebra generated ks ;0 by K i±1 , K it ;0 , k±1 0, and s 1.

4 induces a surjective Z-algebra homomorphism : U → D (n). We also set D (n) = D (n) ∩ D (n) for ∈ {+, −, 0}. , U − ). Hence, + D (n)+ = C (n)+ ⊗Z Z[z+ 1 , z2 , . ] and − D (n)− = C (n)− ⊗Z Z[z− 1 , z2 , . , (u i− )(m) ). 2). 1) is a Z-module isomorphism; see [12, Cor. 50]. In particular, D (n) is a free Z-module. The Z-algebra D (n) gives rise to a Z-form U (n) for U (n), the extended quantum affine sln : U (n) = D (n) ∩ U (n) = C (n)+ D (n)0 C (n)− . 4 in terms of specialization. ks ;0 3 Of course, this fact can be proved directly by the relation [x , y ] = δ s t s,t 1 .

0 0 0 · · · v ±(n−2)s −v ±ns ⎠ 1 1 1 1 1 ∓ [s] ∓ [s] ∓ [s] ··· ∓ [s] ∓ [s] By the definition of hi,±s and θ±s , n hi,±s = n (±s) X i, j g j,±s , for 1 i < n, and θ±s = j =1 (±s) X n, j g j,±s . j =1 A direct calculation shows that det(X (±s) ) = ∓ 1 1 + v ±2s + · · · + v ±2(n−1)s [s] n−2 v ±is = 0 (n (±s) We denote the inverse of X (±s) by Y (±s) = (Yi, j ). Thus, for each 1 n−1 gi,±s = (±s) 2). i=1 i n, (±s) Yi, j h j,±s + Yi,n θ±s . j =1 Therefore, the Q(v)-subspace of U(gln ) spanned by g1,±s , .

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

by Steven

4.1