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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bases for some reciprocity algebras I


Authors: Roger Howe and Soo Teck Lee
Journal: Trans. Amer. Math. Soc. 359 (2007), 4359-4387
MSC (2000): Primary 22E46
Published electronically: March 20, 2007
MathSciNet review: 2309189
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Abstract: For a complex vector space $ V$, let $ \mathcal{P}(V)$ be the algebra of polynomial functions on $ V$. In this paper, we construct bases for the algebra of all $ \operatorname{GL}_n(\mathbb{C})\times \operatorname{GL}_{m_1} (\mathbb{C})\tim... ..._2} (\mathbb{C})\times\cdot\cdot\cdot\times \operatorname{GL}_{m_r}(\mathbb{C})$ highest weight vectors in $ \mathcal{P}\left(\mathbb{C}^n\otimes \mathbb{C}^m\right)$, where $ m=m_1+\cdot\cdot\cdot+m_r$ and $ m_j\leq n$ for all $ 1\leq j\leq r$, and the algebra of $ \operatorname{GL}_n(\mathbb{C})\times \operatorname{GL}_k(\mathbb{C})\times\operatorname{GL}_1(\mathbb{C})$ highest weight vectors in $ \mathcal{P}\left[\left(\mathbb{C}^n\otimes\mathbb{C}^k\right)\oplus \left(\mathbb{C}^n{}^\ast\otimes\mathbb{C}^l\right)\right]$.


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Additional Information

Roger Howe
Affiliation: Department of Mathematics, Yale University New Haven, Connecticut 06520-8283
Email: howe@math.yale.edu

Soo Teck Lee
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
Email: matleest@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04142-6
PII: S 0002-9947(07)04142-6
Received by editor(s): April 8, 2005
Received by editor(s) in revised form: August 22, 2005
Published electronically: March 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.