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"data_source": "DigitalLearningGmbH/MATH-lighteval",
"prompt": [
{
"role": "user",
"content": "Consider a Lie group $G$ and its Lie algebra $\\mathfrak{g}$. For an element $\\mu \\in \\mathfrak{g}^*$, the coadjoint orbit $O_\\mu$ is given by $O_\\mu \\simeq G/G_\\mu$, where $G_\\mu$ is the stabilizer of $\\mu$. Given that there is a symplectic form on each orbit, determine if the orbit is a symplectic manifold. Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model."
}
],
"ability": "math",
"reward_model": {
"style": "rule",
"ground_truth": "Yes"
},
"extra_info": {
"split": "train",
"index": 21747,
"question": "Consider a Lie group $G$ and its Lie algebra $\\mathfrak{g}$. For an element $\\mu \\in \\mathfrak{g}^*$, the coadjoint orbit $O_\\mu$ is given by $O_\\mu \\simeq G/G_\\mu$, where $G_\\mu$ is the stabilizer of $\\mu$. Given that there is a symplectic form on each orbit, determine if the orbit is a symplectic manifold. Let's think step by step and output the final answer within \\boxed{}.\nA part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.",
"transfer_instruction": "A part of your reasoning process will be transferred to another model. Therefore, your reasoning MUST be written clearly and systematically so that it can be easily understood by another model.",
"difficulty": 8.5,
"dataset": "DeepMath-103K"
}
} |