215 citations · 550 across the 60 of their papers we have counts for
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Weyl algebras for quantum homogeneous spaces
Gail Letzter, Siddhartha Sahi, Hadi Salmasian
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmet…
The Capelli eigenvalue problem for quantum groups
Gail Letzter, Siddhartha Sahi, Hadi Salmasian
We introduce and study quantum Capelli operators inside newly constructed quantum Weyl algebras associated to three families of symmetric pairs. Both the center of a particular qua…
Quantized Weyl algebras, the double centralizer property, and a new First Fundamental Theorem for
Gail Letzter, Siddhartha Sahi, Hadi Salmasian
Let denote the quantized coordinate ring of the space of matrices, equipped with natural actions of the quantized enveloping algebr…
Some remarks on non-symmetric interpolation Macdonald polynomials
Siddhartha Sahi, Jasper Stokman
We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolatio…
Double affine Hecke algebras and congruence groups
Bogdan Ion, Siddhartha Sahi
The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/…
Equivariant cohomology and tensor categories
Martin Andler, Siddhartha Sahi
We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermath…
Triple groups and Cherednik algebras
Bogdan Ion, Siddhartha Sahi
The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Hecke algebras. This has as immediate conse…
Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture
Martin Andler, Siddhartha Sahi, Charles Torossian
Consider the Kontsevich -product on the symmetric algebra of a finite dimensional Lie algebra , regarded as the algebra of distributions with support 0 on $\mat…
Kontsevich quantization and invariant distributions on Lie groups
Martin Andler, Alexander Dvorsky, Siddhartha Sahi
We study Kontsevich's deformation quantization for the dual of a finite-dimensional real Lie algebra (or superalgebra) g. In this case the Kontsevich star-product defines a new con…
Deformation quantization and invariant distributions
Martin Andler, Alexander Dvorsky, Siddhartha Sahi
In 1979, M. Kashiwara and M. Vergne formulated a conjecture on a Lie group G which implies that the Duflo isomorphism of Z(g) and S(g)^g extends to a natural module isomorphism bet…
A new formula for weight multiplicities and characters
Siddhartha Sahi
We describe a new formula for weight multiplicities and characters of semisimple Lie algebras. Our formula expresses these weight multiplicities as sums of positive rational number…