## Rogawski’s conjecture on the Jantzen filtration for the degenerate affine Hecke algebra of type A

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- by Takeshi Suzuki
- Represent. Theory
**2**(1998), 393-409 - DOI: https://doi.org/10.1090/S1088-4165-98-00043-0
- Published electronically: October 26, 1998
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## Abstract:

The functors constructed by Arakawa and the author relate the representation theory of $\mathfrak {gl}_n$ and that of the degenerate affine Hecke algebra $H_\ell$ of $\mathrm {GL}_\ell$. They transform the Verma modules over $\mathfrak {gl}_n$ to the standard modules over $H_\ell$. In this paper we prove that they transform the simple modules to the simple modules (in more general situations than in the previous paper). We also prove that they transform the Jantzen filtration on the Verma modules to that on the standard modules. We obtain the following results for the representations of $H_\ell$ by translating the corresponding results for $\mathfrak {gl}_n$ through the functors: (i) the (generalized) Bernstein-Gelfand-Gelfand resolution for a certain class of simple modules, (ii) the multiplicity formula for the composition series of the standard modules, and (iii) its refinement concerning the Jantzen filtration on the standard modules, which was conjectured by Rogawski.## References

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## Bibliographic Information

**Takeshi Suzuki**- Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Japan
- MR Author ID: 199324
- Email: takeshi@kurims.kyoto-u.ac.jp
- Received by editor(s): January 23, 1998
- Received by editor(s) in revised form: August 31, 1998
- Published electronically: October 26, 1998
- Additional Notes: The author is supported by the JSPS Research Fellowships for Young Scientists.
- © Copyright 1998 American Mathematical Society
- Journal: Represent. Theory
**2**(1998), 393-409 - MSC (1991): Primary 22E50; Secondary 17B10
- DOI: https://doi.org/10.1090/S1088-4165-98-00043-0
- MathSciNet review: 1651408