Dual Canonical Bases for the Quantum Special Linear Group and Invariant Subalgebras

نویسندگان

  • HECHUN ZHANG
  • R. B. ZHANG
چکیده

Abstract. A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible Uq(sl(n))-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quantum minors.

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

Dual Canonical Bases for the Quantum General Linear Supergroup

Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup Oq(SLm|n). We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translati...

متن کامل

ar X iv : q - a lg / 9 71 20 46 v 2 2 8 Se p 19 98 Web bases for sl ( 3 ) are not dual canonical

or its invariant space Inv(V1 ⊗ V2 ⊗ . . .⊗ Vn). The quantum group Uq(g) has representations and vector spaces of invariants which generalize these, and one can also study their bases, with or without the intention of specializing to q = 1. (For simplicity, we will usually consider Uq(g) as an algebra over C(q ), and we will only occassionally mention Z[q] as a ground ring.) Lusztig’s remarkabl...

متن کامل

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

متن کامل

On Dual Canonical Bases

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...

متن کامل

Canonical bases for subalgebras of factor algebras

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

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 2005