Affine Centralizer Algebras for $\boldsymbol{G_2}$
نویسندگان
چکیده
منابع مشابه
Matrix Units for Centralizer Algebras
We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’...
متن کاملDegenerate two-boundary centralizer algebras
Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra g on tensor space of the form M ⊗ N ⊗ V ⊗k. We define the degenerate two-boundary braid group Gk and show that centrali...
متن کاملCharacters of Brauer's Centralizer Algebras
Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...
متن کاملDegenerate affine Hecke algebras and centralizer construction for the symmetric groups
In our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We study the ‘stable’ properties of the centralizers of S(n − m) in the group algebra C[S(n)] as n → ∞ with m fixed. We construct a limit centralizer algebra A...
متن کاملComputing the Discriminants of Brauer's Centralizer Algebras
This paper discusses a computational problem arising in the study of the structure theory of Brauer's orthogonal and symplectic centralizer algebras. The problem is to compute the ranks of certain combinatorially defined matrices Zm k(x) (these matrices are presented in §2). This computation is difficult because the sizes of the matrices Zm k(x) are enormous even for small values of m and k . H...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx223