Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2016
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1611.06968 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911949507264512 |
|---|---|
| author | King, Oliver H. Martin, Paul P. Parker, Alison E. |
| author_facet | King, Oliver H. Martin, Paul P. Parker, Alison E. |
| contents | The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex numbers. We determine Gram determinants for the cell modules with respect to a canonical contravariant form. We show in particular that the algebra is semisimple over the complex numbers unless at least one of the "quantisation" parameters, or the sum or difference of two of these parameters is integral, or the bulk parameter $q$ is a root of unity. We find decomposition numbers in many of the $q$-generic cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_06968 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Decomposition matrices and blocks for the symplectic blob algebra over the complex field King, Oliver H. Martin, Paul P. Parker, Alison E. Representation Theory 05E15, 16G99, 20G05 and 20G08 The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex numbers. We determine Gram determinants for the cell modules with respect to a canonical contravariant form. We show in particular that the algebra is semisimple over the complex numbers unless at least one of the "quantisation" parameters, or the sum or difference of two of these parameters is integral, or the bulk parameter $q$ is a root of unity. We find decomposition numbers in many of the $q$-generic cases. |
| title | Decomposition matrices and blocks for the symplectic blob algebra over the complex field |
| topic | Representation Theory 05E15, 16G99, 20G05 and 20G08 |
| url | https://arxiv.org/abs/1611.06968 |