A functional realization of the Gelfand-Tsetlin base
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912644840030208 |
|---|---|
| author | Artamonov, D. V. |
| author_facet | Artamonov, D. V. |
| contents | In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin diagrams are linear combinations of some new functions of hypergeometric type which are closely related to $A$-hypergeometric functions. These new functions are solution of a system of partial differential equations which one obtains from the Gelfand-Kapranov-Zelevinsky by an "antisymmetrization". The coefficients in the constructed linear combination are hypergeometric constants i.e. they are values of some hypergeometric functions when instead of all arguments ones are substituted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12680 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A functional realization of the Gelfand-Tsetlin base Artamonov, D. V. Representation Theory Complex Variables In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin diagrams are linear combinations of some new functions of hypergeometric type which are closely related to $A$-hypergeometric functions. These new functions are solution of a system of partial differential equations which one obtains from the Gelfand-Kapranov-Zelevinsky by an "antisymmetrization". The coefficients in the constructed linear combination are hypergeometric constants i.e. they are values of some hypergeometric functions when instead of all arguments ones are substituted. |
| title | A functional realization of the Gelfand-Tsetlin base |
| topic | Representation Theory Complex Variables |
| url | https://arxiv.org/abs/2210.12680 |