Knop F (1997)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1997
Publisher: European Mathematical Society / Springer Verlag (Germany)
Book Volume: 72
Pages Range: 84-100
Journal Issue: 1
DOI: 10.4171/CMH/72.1.7
We introduce families of symmetric and non-symmetric polynomials (the quantum Capelli polynomials) which depend on two parameters q and t, They are defined in terms of vanishing conditions, In the differential limit (q = t(alpha) and t --> 1) they are related to Capelli identities. It is shown that the quantum Capelli polynomials form an eigenbasis for certain q-difference operators. As a corollary, we obtain that the top homogeneous part is a symmetric/non-symmetric Macdonald polynomial. Furthermore, we study the vanishing and integrality properties of the quantum Capelli polynomials.
APA:
Knop, F. (1997). Symmetric and non-symmetric quantum Capelli polynomials. Commentarii Mathematici Helvetici, 72(1), 84-100. https://dx.doi.org/10.4171/CMH/72.1.7
MLA:
Knop, Friedrich. "Symmetric and non-symmetric quantum Capelli polynomials." Commentarii Mathematici Helvetici 72.1 (1997): 84-100.
BibTeX: Download