Symmetric functions and Springer representations
| Autor: | Syu Kato |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
General Mathematics
Mathematics - Quantum Algebra FOS: Mathematics Mathematics - Combinatorics Quantum Algebra (math.QA) Combinatorics (math.CO) Representation Theory (math.RT) Mathematics - Commutative Algebra Mathematics::Representation Theory Commutative Algebra (math.AC) Mathematics - Representation Theory |
| Zdroj: | Indagationes Mathematicae. 33:255-278 |
| ISSN: | 0019-3577 |
| Popis: | The characters of the (total) Springer representations are identified with the Green functions by Kazhdan [Israel J. Math. {\bf 28} (1977)], and the latter are identified with Hall-Littlewood's $Q$-functions by Green [Trans. Amer. Math. Soc. (1955)]. In this paper, we present a purely algebraic proof that the (total) Springer representations of $\mathop{GL} ( n )$ are $\mathrm{Ext}$-orthogonal to each other, and show that it is compatible with the natural categorification of the ring of symmetric functions. Comment: 26pp, v2: corrected an error in the proof of (old) Proposition 2.28, v3: streamlined the exposition, final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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