On O m ×G L n Highest Weight Vectors

Helmer Aslaksen (), Eng-Chye Tan () and Chen-bo Zhu ()
Additional contact information
Helmer Aslaksen: National University of Singapore, Department of Mathematics
Eng-Chye Tan: National University of Singapore, Department of Mathematics
Chen-bo Zhu: National University of Singapore, Department of Mathematics

A chapter in Symmetries in Science VIII, 1995, pp 1-11 from Springer

Abstract: Abstract Let ℂm,n be the vector space of m×n complex matrices and P(ℂm,n) be the algebra of complex-valued polynomials on ℂm,n. Let GL m ×GL n act on P(ℂm,n) by pre-and post-multiplication as follows: $$\left( {{g_1},{g_2}} \right)f\left( x \right) = f\left( {g_1^{ - 1}x{g_2}} \right)$$ where x ∈ ℂm,n, (g 1,g 2) ∈ GL m ×GL n,f ∈ P(ℂm,n). We choose a system of coordinates on ℂm,n as follows: $$\left[ {\begin{array}{*{20}{c}}{{x_{11}}}{{x_{12}}} \ldots {{x_{1n}}} \\{{x_{21}}}{{x_{22}}} \ldots {{x_{2n}}} \\\vdots \vdots \cdots \vdots \\{{x_{m1}}}{{x_{m2}}} \cdots {{x_{mn}}}\end{array}} \right]$$

Keywords: Polynomial Algebra; Root Vector; Positive System; High Weight Vector; Borel Subalgebra (search for similar items in EconPapers)
Date: 1995
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-1915-7_1

Ordering information: This item can be ordered from
http://www.springer.com/9781461519157

DOI: 10.1007/978-1-4615-1915-7_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().