相关论文: Deformed universal characters for classical and af…
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker…
We introduce a new operator $\Gamma$ on symmetric functions, which enables us to obtain a creation formula for Macdonald polynomials. This formula provides a connection between the theory of Macdonald operators initiated by Bergeron,…
For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-character varieties. We restrict the…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…
In this paper, we introduce the Rogers-Szeg\"o deformed $q$-differential operators g$_{n}(bD_{q}|u)$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators g$_{n}(bD_{q})$ is that their limit turns out to…
The article targets binomial ideals in quantum tori and quantum affine spaces. First, noncommutative analogs of known results for commutative (Laurent) polynomial rings are obtained, including the following: Under the assumption of an…
Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We construct a basis of $\U^+$ which is related to the Kashiwara-Lusztig global crystal basis…
We give an explicit, nonnegative formula for the expansion of nonsymmetric Macdonald polynomials specialized at $t=0$ in terms of Demazure characters. Our formula results from constructing Demazure crystals whose characters are the…
For a minimal affinization over a quantum loop algebra of type BC, we provide a character formula in terms of Demazure operators and multiplicities in terms of crystal bases. We also provide a simple formula for the limit of characters.…
The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W_\infty. q-star products and q-Moyal brackets corresponding to these algebras are…
We investigate one-parameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the L\^{e} numbers of the…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems ($ABCD$) with respect to the integer and root lattices. As a result, we obtain a full description of…
The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of $gl_n$. Earlier work of Kirillov and Reshetikhin proposed a generalization of these identities to the other classical Lie algebras,…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
Let G be a symplectic or orthogonal complex Lie group with Lie algebra g. As a G-module, the decomposition of the symmetric algebra S(g) into its irreducible components can be explicitely obtained by using identities due to Littlewood. We…