Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

A Hydro Wheel System in A Non-Natural Pond Using Renewable

One of the most cost-effective ways to generate electricity is through waterwheels. Because of the need for clean energy and sustainable electricity production, hydropower currently plays an important role in meeting energy demand. Although water wheels were studied academically as early as the eighteenth century, they were mostly ignored until the twentieth century. Only in the last two decades has there been a revived interest in their use among scientists. The researcher came up with this topic to discuss its benefits and how it will be beneficial in our daily lives and make our surroundings safe, which needs enough light and helps the school or park premises lighten up the dark areas at night. Having enough illumination inside the premises of in schools and parks, according to numerous sources and data gathering findings, will help folks become comfortable in the location they are staying or visiting. Good illumination can help with mobility, safety, and security