Bases for some reciprocity algebras I
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- by Roger Howe and Soo Teck Lee PDF
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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 $\operatorname {GL}_n(\mathbb {C})\times \operatorname {GL}_{m_1} (\mathbb {C})\times \operatorname {GL}_{m_2} (\mathbb {C})\times \cdot \cdot \cdot \times \operatorname {GL}_{m_r}(\mathbb {C})$ 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 $\mathcal {P}\left [\left (\mathbb {C}^n\otimes \mathbb {C}^k\right )\oplus \left (\mathbb {C}^n{}^\ast \otimes \mathbb {C}^l\right )\right ]$.References
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Additional Information
- Roger Howe
- Affiliation: Department of Mathematics, Yale University New Haven, Connecticut 06520-8283
- MR Author ID: 88860
- ORCID: 0000-0002-5788-0972
- 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
- Received by editor(s): April 8, 2005
- Received by editor(s) in revised form: August 22, 2005
- Published electronically: March 20, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4359-4387
- MSC (2000): Primary 22E46
- DOI: https://doi.org/10.1090/S0002-9947-07-04142-6
- MathSciNet review: 2309189