Journal article
W-graph versions of tensoring with the defining representation
Journal of algebraic combinatorics, v 34(4), pp 545-585
2011
Abstract
We further develop the theory of inducing
W
-graphs worked out by Howlett and Yin (Math. Z. 244(2):415–431,
2003
and Manuscr. Math. 115(4):495–511,
2004
), focusing on the case
. Our main application is to give two
W
-graph versions of tensoring with the
defining representation
V
, one being
for
the Hecke algebras of
and the other
, where
is a subalgebra of the extended affine Hecke algebra and the subscript signifies taking the degree 1 part. We look at the corresponding
W
-graph versions of the projection
V
⊗
V
⊗−→
S
2
V
⊗−. This does not send canonical basis elements to canonical basis elements, but we show that it approximates doing so as the Hecke algebra parameter
u
→0. We make this approximation combinatorially explicit by determining it on cells and relate this to RSK growth diagrams.
Metrics
Details
- Title
- W-graph versions of tensoring with the defining representation
- Creators
- Jonah Blasiak - University of Michigan–Ann Arbor
- Publication Details
- Journal of algebraic combinatorics, v 34(4), pp 545-585
- Publisher
- Springer US
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000295865500001
- Scopus ID
- 2-s2.0-85027923078
- Other Identifier
- 991021862387604721
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- Web of Science research areas
- Mathematics