Quantized mixed tensor space and Schur–Weyl duality I

نویسندگان

  • R. Dipper
  • S. Doty
  • F. Stoll
چکیده

This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quantized mixed tensor space and Schur–Weyl duality II

In this paper, we show the second part of Schur-Weyl duality for mixed tensor space. The quantum group U = U(gln) of the general linear group and a q-deformation Br,s(q) of the walled Brauer algebra act on V ⊗r ⊗V ∗⊗s where V = R is the natural U-module. We show that EndBnr,s(q)(V ⊗r ⊗ V ∗) is the image of the representation of U, which we call the rational q-Schur algebra. As a byproduct, we o...

متن کامل

The Envelope of Symmetry on Tensors and Characteristic Free Schur-weyl Duality

The envelope of the action of the symmetric group Sr on rank r tensors has dimension independent of the characteristic of the base field. M. Härterich proved this, using G.E. Murphy’s combinatorial basis of the Hecke algebra of Sr in order to describe an explicit basis for the the annihilator of tensor space. This leads to a proof of Schur-Weyl duality in positive characteristic, assuming the c...

متن کامل

8 M ay 2 00 8 SCHUR – WEYL DUALITY OVER FINITE FIELDS

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has more than r elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if dimV is at least r + 1 then the natural map kSr → EndGL(V )(V ) is an isomorphism; this isomorphism may fail if dimk(V ) is not strictly larger than r.

متن کامل

ar X iv : 0 80 5 . 12 35 v 2 [ m at h . G R ] 3 0 Ju n 20 09 SCHUR – WEYL DUALITY OVER FINITE FIELDS

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has at least r + 1 elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if the dimension of V is at least r + 1, the natural map kSr → EndGL(V )(V ) is an isomorphism. This isomorphism may fail if dimk V is not strictly larger than r.

متن کامل

Bmw Algebra, Quantized Coordinate Algebra and Type C Schur–weyl Duality

We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra Bn(−q , q) and the quantum algebra associated to the symplectic Lie algebra sp2m. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang ([37]) in the symplectic case. As a byproduct, we show tha...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009