Research output: Contribution to journal › Article
Finite traces and representations of the group of infinite matrices over a finite field. / Gorin, V.; Vershik, A.
In: Advances in Mathematics, Vol. 254, 2014, p. 331-395.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Finite traces and representations of the group of infinite matrices over a finite field
AU - Gorin, V.
AU - Vershik, A.
PY - 2014
Y1 - 2014
N2 - The article is devoted to the representation theory of locally compact infinite-dimensional group GLB of almost upper-triangular infinite matrices over the finite field with q elements. This group was defined by S.K., A.V., and Andrei Zelevinsky in 1982 as an adequate n = infinity analogue of general linear groups GL(n, q). It serves as an alternative to GL(infinity, q), whose representation theory is poor.Our most important results are the description of semifinite unipotent traces (characters) of the group GLB. via certain probability measures on the Borel subgroup B and the construction of the corresponding von Neumann factor representations of type H-infinity.As a main tool we use the subalgebra A(GLB) of smooth functions in the group algebra L-1 (GLB). This subalgebra is an inductive limit of the finite-dimensional group algebras C(GL(n, q)) under parabolic embeddings.As in other examples of the asymptotic representation theory we discover remarkable properties of the infinite case which does not take pl
AB - The article is devoted to the representation theory of locally compact infinite-dimensional group GLB of almost upper-triangular infinite matrices over the finite field with q elements. This group was defined by S.K., A.V., and Andrei Zelevinsky in 1982 as an adequate n = infinity analogue of general linear groups GL(n, q). It serves as an alternative to GL(infinity, q), whose representation theory is poor.Our most important results are the description of semifinite unipotent traces (characters) of the group GLB. via certain probability measures on the Borel subgroup B and the construction of the corresponding von Neumann factor representations of type H-infinity.As a main tool we use the subalgebra A(GLB) of smooth functions in the group algebra L-1 (GLB). This subalgebra is an inductive limit of the finite-dimensional group algebras C(GL(n, q)) under parabolic embeddings.As in other examples of the asymptotic representation theory we discover remarkable properties of the infinite case which does not take pl
U2 - 10.1016/j.aim.2013.12.028
DO - 10.1016/j.aim.2013.12.028
M3 - Article
VL - 254
SP - 331
EP - 395
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
ER -
ID: 7036965