1. CJM 2013 (vol 66 pp. 566)
 Choiy, Kwangho

Transfer of Plancherel Measures for Unitary Supercuspidal Representations between $p$adic Inner Forms
Let $F$ be a $p$adic field of characteristic $0$, and let $M$ be an $F$Levi subgroup of a connected reductive $F$split group such that $\Pi_{i=1}^{r} SL_{n_i} \subseteq M \subseteq \Pi_{i=1}^{r} GL_{n_i}$ for positive integers $r$ and $n_i$. We prove that the Plancherel measure for any unitary supercuspidal representation of $M(F)$ is identically transferred under the local JacquetLanglands type correspondence between $M$ and its $F$inner forms, assuming a working hypothesis that Plancherel measures are invariant on a certain set. This work extends the result of
MuiÄ and Savin (2000) for Siegel Levi subgroups of the groups $SO_{4n}$ and $Sp_{4n}$ under the local JacquetLanglands correspondence. It can be applied to a simply connected simple $F$group of type $E_6$ or $E_7$, and a connected reductive $F$group of type $A_{n}$, $B_{n}$, $C_n$ or $D_n$.
Keywords:Plancherel measure, inner form, local to global global argument, cuspidal automorphic representation, JacquetLanglands correspondence Categories:22E50, 11F70, 22E55, 22E35 

2. CJM 2011 (vol 64 pp. 1090)
 Rosso, Daniele

Classic and Mirabolic RobinsonSchenstedKnuth Correspondence for Partial Flags
In this paper we first generalize to the case of
partial flags a result proved both by Spaltenstein and by Steinberg
that relates the relative position of two complete flags and the
irreducible components of the flag variety in which they lie, using
the RobinsonSchenstedKnuth correspondence. Then we use this result
to generalize the mirabolic RobinsonSchenstedKnuth correspondence
defined by Travkin, to the case of two partial flags and a line.
Keywords:partial flag varieties, RSK correspondence Categories:14M15, 05A05 

3. CJM 2009 (vol 62 pp. 94)
4. CJM 2004 (vol 56 pp. 495)
 Gomi, Yasushi; Nakamura, Iku; Shinoda, Kenichi

Coinvariant Algebras of Finite Subgroups of $\SL(3,C)$
For most of the finite subgroups of $\SL(3,\mathbf{C})$, we give explicit formulae for
the Molien series of the coinvariant algebras, generalizing McKay's formulae
\cite{M99} for subgroups of $\SU(2)$. We also study the $G$orbit Hilbert scheme
$\Hilb^G(\mathbf{C}^3)$ for any finite subgroup $G$ of $\SO(3)$, which is known to be a
minimal (crepant) resolution of the orbit space $\mathbf{C}^3/G$. In this case the fiber
over the origin of the HilbertChow morphism from $\Hilb^G(\mathbf{C}^3)$ to $\mathbf{C}^3/G$
consists of finitely many smooth rational curves, whose planar dual graph is
identified with a certain subgraph of the representation graph of $G$. This is
an $\SO(3)$ version of the McKay correspondence in the $\SU(2)$ case.
Keywords:Hilbert scheme, Invariant theory, Coinvariant algebra,, McKay quiver, McKay correspondence Categories:14J30, 14J17 

5. CJM 2000 (vol 52 pp. 695)
 Carey, A.; Farber, M.; Mathai, V.

Correspondences, von Neumann Algebras and Holomorphic $L^2$ Torsion
Given a holomorphic Hilbertian bundle on a compact complex manifold, we
introduce the notion of holomorphic $L^2$ torsion, which lies in the
determinant line of the twisted $L^2$ Dolbeault cohomology and
represents a volume element there. Here we utilise the theory of
determinant lines of Hilbertian modules over finite von~Neumann
algebras as developed in \cite{CFM}. This specialises to the
RaySingerQuillen holomorphic torsion in the finite dimensional case.
We compute a metric variation formula for the holomorphic $L^2$
torsion, which shows that it is {\it not\/} in general independent of
the choice of Hermitian metrics on the complex manifold and on the
holomorphic Hilbertian bundle, which are needed to define it. We
therefore initiate the theory of correspondences of determinant lines,
that enables us to define a relative holomorphic $L^2$ torsion for a
pair of flat Hilbertian bundles, which we prove is independent of the
choice of Hermitian metrics on the complex manifold and on the flat
Hilbertian bundles.
Keywords:holomorphic $L^2$ torsion, correspondences, local index theorem, almost KÃ¤hler manifolds, von~Neumann algebras, determinant lines Categories:58J52, 58J35, 58J20 

6. CJM 1999 (vol 51 pp. 850)
 Muhly, Paul S.; Solel, Baruch

Tensor Algebras, Induced Representations, and the Wold Decomposition
Our objective in this sequel to \cite{MSp96a} is to develop extensions,
to representations of tensor algebras over $C^{*}$correspondences, of
two fundamental facts about isometries on Hilbert space: The Wold
decomposition theorem and Beurling's theorem, and to apply these to
the analysis of the invariant subspace structure of certain subalgebras
of CuntzKrieger algebras.
Keywords:tensor algebras, correspondence, induced representation, Wold decomposition, Beurling's theorem Categories:46L05, 46L40, 46L89, 47D15, 47D25, 46M10, 46M99, 47A20, 47A45, 47B35 
