Green Functions Associated to Complex Reflection Groups

By Toshiaki Shoji. 2001

50 citations recorded by the source corpus.

Abstract Green functions of classical groups are determined by the data from Weyl groups and by certain combinatorial objects called symbols. Generalizing this, we define Green functions associated to complex reflection groups G(e, 1, n) and study their combinatorial properties. We construct Hall–Littlewood functions and Schur functions in our scheme and show that such Green functions are obtained as a transition matrix between those two symmetric functions, as in the case of GLn.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e11238464e33b761e2ebd82c8098aa0022fbccb

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In Discrete Mathematics and Combinatorics

1. Arun Ram
2. Kendra Nelsen
3. James Parkinson
4. Aaron D. Lauda

In Geometry and Topology

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2. Kendra Nelsen
3. Stephen Griffeth
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In Mathematical Physics

1. Arun Ram
2. Kendra Nelsen
3. James Parkinson
4. Stephen Griffeth
5. I. Gordon

Citations in the corpus

• Surveys in Combinatorics 2003: Kostka–Foulkes polynomials and Macdonald spherical functions (2003, background): “The connection to Springer representations of Weyl groups and the representations of Chevalley groups over finite fields has been developed extensively by Lusztig, Shoji and others; a good survey of the current theory is in [18] and the recent papers [ 19 ] show how this theory is beginning to exten”