| A Class of Standard Bases of Polynomial Algebras and Its Applications |
| Received:January 15, 2007 Revised:March 08, 2008 |
| Key Words:
standard basis quantum group Clebsch-Gordan formula Grothendieck ring.
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| Fund Project:the National Natural Science Foundation of China (Nos.10471121; 10771182; 10771183); Sino-German Project (No.GZ310); Nanjing Agricultural University Youth Science and Technology Innovation Foundation (No.KJ05028). |
| Author Name | Affiliation | | DONG Jing Cheng | School of Mathematics, Yangzhou University, Jiangsu 225002, China
College of Engineering, Nanjing Agricultural University, Jiangsu 210031, China | | LI Li Bin | School of Mathematics, Yangzhou University, Jiangsu 225002, China | | CHEN Hui Xiang | School of Mathematics, Yangzhou University, Jiangsu 225002, China |
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| Abstract: |
| Let $H={\cal U}_q({\rm sl}(2))$ or ${\cal U}({\rm sl}(2))$. By means of the standard basis of polynomial algebras, the Clebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of $V(1)^{\otimes n}$ into the direct sum of simple modules is given in this paper. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.02.001 |
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