Article Associative Rings and Algebras Commutative Rings and Algebras Mathematics Mathematics and Statistics Non-associative Rings and Algebras
The nonstandard Hecke algebra
ℋ
̌
r
was defined by Mulmuley and Sohoni to study the Kronecker problem. We study a quotient
ℋ
̌
r
,
2
of
ℋ
̌
r
, called the nonstandard Temperley–Lieb algebra, which is a subalgebra of the symmetric square of the Temperley–Lieb algebra TL
r
. We give a complete description of its irreducible representations. We find that the restriction of an irreducible
ℋ
̌
r
,
2
-module to
ℋ
̌
r
−
1
,
2
is multiplicity-free, and as a consequence, any irreducible
ℋ
̌
r
,
2
-module has a seminormal basis that is unique up to a diagonal transformation.
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Details
Title
Representation Theory of the Nonstandard Hecke Algebra
Creators
Jonah Blasiak - Drexel University
Publication Details
Algebras and representation theory, v 18(3), pp 585-612
Publisher
Springer Netherlands
Resource Type
Journal article
Language
English
Academic Unit
Mathematics
Web of Science ID
WOS:000356541100001
Scopus ID
2-s2.0-84931573459
Other Identifier
991019168183904721
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