| Title:
|
Further determinant identities related to classical root systems (English) |
| Author:
|
Chu, Wenchang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
981-987 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems. (English) |
| Keyword:
|
Vandermonde determinant |
| Keyword:
|
symmetric function |
| Keyword:
|
classical root system |
| MSC:
|
05E05 |
| MSC:
|
15A15 |
| idZBL:
|
Zbl 06819567 |
| idMR:
|
MR3736013 |
| DOI:
|
10.21136/CMJ.2017.0265-16 |
| . |
| Date available:
|
2017-11-20T14:54:24Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146961 |
| . |
| Reference:
|
[1] Bhatnagar, G.: A short proof of an identity of Sylvester.Int. J. Math. Math. Sci. 22 (1999), 431-435. Zbl 0929.01019, MR 1695300, 10.1155/S0161171299224313 |
| Reference:
|
[2] Chu, W.: Divided differences and symmetric functions.Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 2 (1999), 609-618. Zbl 0935.05088, MR 1719558 |
| Reference:
|
[3] Chu, W.: Determinants and algebraic identities associated with the root systems of classical Lie algebras.Commun. Algebra 42 (2014), 3619-3633. Zbl 1291.05208, MR 3196066, 10.1080/00927872.2013.790394 |
| Reference:
|
[4] Chu, W., Claudio, L. V. Di: The Vandermonde determinant and generalizations associated with the classical Lie algebras.Ital. J. Pure Appl. Math. 20 (2006), 139-158 Italian. Zbl 1150.15005, MR 2247418 |
| Reference:
|
[5] Dyson, F. J.: Statistical theory of the energy levels of complex systems. I.J. Math. Phys. 3 (1962), 140-156. Zbl 0105.41604, MR 0143556, 10.1063/1.1703773 |
| Reference:
|
[6] Fulton, W., Harris, J.: Representation Theory.Graduate Texts in Mathematics 129, Springer, New York (1991). Zbl 0744.22001, MR 1153249, 10.1007/978-1-4612-0979-9 |
| Reference:
|
[7] Good, I. J.: Short proof of a conjecture by Dyson.J. Math. Phys. 11 (1970), 1884. MR 0258644, 10.1063/1.1665339 |
| Reference:
|
[8] Gross, K. I., Richards, D. St. P.: Constant term identities and hypergeometric functions on spaces of Hermitian matrices.J. Stat. Plann. Inference 34 (1993), 151-158. Zbl 0767.33010, MR 1209996, 10.1016/0378-3758(93)90040-D |
| Reference:
|
[9] Macdonald, I. G.: Symmetric Functions and Hall Polynomials.Oxford Mathematical Monographs, Clarendon Press, Oxford (1979). Zbl 0487.20007, MR 0553598 |
| . |
