Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1
In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin crystal B n;1 of type D (1) n . They have a commuting family of time evolutions and solitons of length l are labeled by U q (A (1) n1 )-crystal B 2;l A . The scattering rule of two solitons of le...
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| Format: | Thesis |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/2542/ http://eprints.uthm.edu.my/2542/1/24p%20MAHATHIR%20MOHAMAD.pdf |
| _version_ | 1848887767047602176 |
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| author | Mohamad, Mahathir |
| author_facet | Mohamad, Mahathir |
| author_sort | Mohamad, Mahathir |
| building | UTHM Institutional Repository |
| collection | Online Access |
| description | In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin
crystal B
n;1
of type D
(1)
n
. They have a commuting family of time evolutions and
solitons of length l are labeled by U
q
(A
(1)
n1
)-crystal B
2;l
A
. The scattering rule of two
solitons of lengths l
1
and l
2
(l
1
> l
) including the phase shift is identified with the
combinatorial R-matrix for the U
q
2
(A
(1)
n1
)-crystal B
2;l
A
2
B
2;l
A
1
. In part 2 we consider
the Kirrilov-Reshetikhin crystal B
6;1
for the exceptional affine type E
. We will
give a conjecture on a statistic-preserving bijection between the highest weight paths
consisting of B
6;1
and the corresponding rigged configuration. The algorithm only uses
the structure of the crystal graph, hence could also be applied for other exceptional
types. Our B
6;1
has a different algorithm compared our B
1;1
because we must consider
the element Ø, unique element in the highest weight crystal of weight 0, in the crystal
graph. We will give many examples supporting the conjecture.
(1)
6 |
| first_indexed | 2025-11-15T19:59:37Z |
| format | Thesis |
| id | uthm-2542 |
| institution | Universiti Tun Hussein Onn Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T19:59:37Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | uthm-25422021-11-01T02:38:02Z http://eprints.uthm.edu.my/2542/ Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 Mohamad, Mahathir QA150-272.5 Algebra In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin crystal B n;1 of type D (1) n . They have a commuting family of time evolutions and solitons of length l are labeled by U q (A (1) n1 )-crystal B 2;l A . The scattering rule of two solitons of lengths l 1 and l 2 (l 1 > l ) including the phase shift is identified with the combinatorial R-matrix for the U q 2 (A (1) n1 )-crystal B 2;l A 2 B 2;l A 1 . In part 2 we consider the Kirrilov-Reshetikhin crystal B 6;1 for the exceptional affine type E . We will give a conjecture on a statistic-preserving bijection between the highest weight paths consisting of B 6;1 and the corresponding rigged configuration. The algorithm only uses the structure of the crystal graph, hence could also be applied for other exceptional types. Our B 6;1 has a different algorithm compared our B 1;1 because we must consider the element Ø, unique element in the highest weight crystal of weight 0, in the crystal graph. We will give many examples supporting the conjecture. (1) 6 2012-03 Thesis NonPeerReviewed text en http://eprints.uthm.edu.my/2542/1/24p%20MAHATHIR%20MOHAMAD.pdf Mohamad, Mahathir (2012) Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1. Doctoral thesis, Osaka University. |
| spellingShingle | QA150-272.5 Algebra Mohamad, Mahathir Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title | Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title_full | Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title_fullStr | Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title_full_unstemmed | Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title_short | Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 |
| title_sort | soliton cellular automata constructed from a uq(dn[1])-crystal bn,1 and kirillov-reshetikhin type bijection for uq(e6[1])-crystal b6,1 |
| topic | QA150-272.5 Algebra |
| url | http://eprints.uthm.edu.my/2542/ http://eprints.uthm.edu.my/2542/1/24p%20MAHATHIR%20MOHAMAD.pdf |