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.  
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 NameAffiliation
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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