Rigid Surface Operator and Symbol Invariant of Partitions
Abstract
The symbol is used to describe the Springer correspondence for the classical groups by Lusztig. We refine the explanation that the $S$-duality maps of the rigid surface operators are symbol preserving maps. And we find that the maps $X_S$ and $Y_S$ used in the construction of $S$-duality maps are essentially the same. We clear up cause of the mismatch problem of the total number of the rigid surface operators between the $B_n$ and $C_n$ theories. And we construct all the $B_n/C_n$ rigid surface operators which can not have a dual. A classification of the problematic surface operators is made.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2017
- DOI:
- 10.48550/arXiv.1711.03463
- arXiv:
- arXiv:1711.03463
- Bibcode:
- 2017arXiv171103463L
- Keywords:
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- Mathematical Physics
- E-Print:
- 27 pages, 30 figures and 6 tables, typo corrected, english improved. arXiv admin note: text overlap with arXiv:1708.07388