Construction of the Symbol Invariant of Partition
Abstract
Symbol is used to describe the Springer correspondence for the classical groups. We prove two structure theorems of symbol. We propose a construction of the symbol of the rigid partitions in the $B_n$, $C_n$, and $D_n$ theories. This construction is natural and consists of two basic building blocks. Using this construction, we give closed formulas of symbols for the rigid partitions in the $B_n, C_n$, and $D_n$ theories. One part of the closed formula is universal and other parts are determined by the specific theory. A comparison of between this closed formula and the old one is made. Previous results can be illustrated more clearly by this closed formula.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2017
- DOI:
- 10.48550/arXiv.1708.07090
- arXiv:
- arXiv:1708.07090
- Bibcode:
- 2017arXiv170807090S
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 27 pages